The Traveller Book is definitely Classic
Traveller. (Everything published by GDW up through the start of
MegaTraveller is Classic
Traveller as far as I know.)
Your best, and most amazing, source for comparison between the editions of Classic Traveller are Frank Filz's
Traveller: Section by Section Comparison. Check it out.
Your question is a little tricky because there are two editions of LBBS 1-3 (1977 and 1981), each similar in many way, but also with differences.
(Here are two posts about the differences between the 1977 and 1981 editions:
Two Points Where I Prefer the 1977 Edition Over the 1981 Edition
Another Difference Between the 1977 Edition and the 1981 Edition
The Traveller Book is almost identical to the 1981 edition of Books 1-3 in terms of
rules. The most notable rules differences between LBBs (1981) and
The Traveller Book is that
The Traveller Book contains the Special Circumstances DMs for combat (like Cover, Concealment, Darkness and so on.)
My own take is that there are differences between LBBs 1981 and
The Traveller Book that go beyond "the rules." They are found in the additional content found in
The Traveller Book and in the rewritten text.
The biggest differences then are the fact that LBBs (both editions) have no mention of any specific setting. There are implied setting details, of course, but no mention of any setting official or otherwise. The back cover text of the boxes as well as the text within the books makes plain that the rules are there for the Referee to create any SF-themed setting he wishes. (The rules for creating subsectors are there for making one's own setting, of course.)
On the other hand
The Traveller Book culminates with an entire section on playing in the Third Imperium. A subsector maps are provided, details about the Third Imperium are provided, adventures in the Third Imperium, details about MegaCorporations, and so on. The structure of the book suggests that one reads the rules
in preparation to play in the Third Imperium. Whether this is good or bad isn't an issue. The point is, it's different.
Moreover, there are slight changes in the text which change the connotation of the sense of play implied by the different editions.
Here are the first three sentences from Book 1:
Traveller deals with a common theme of science-fiction: the concept that an expanding technology will enable us to reach the stars and to populate the worlds which orbit them. The major problem, however, will be that communication, be it political, diplomatic, commercial, or private, will be reduced to the level of the 18th century, reduced to the speed of transportation. The result is a large (bordering on the infinite) universe ripe for the adventurer's bold travels. Using this set of three books, players can play single scenarios or entire adventuring campaigns set in any science-fiction situation.
When I read that passage, the focus I get is on the lack of communication, the distances mattering, and a great expanse of space that may or may not be "civilized," with plenty of room for bold travellers to go have adventures.
Here are the first few sentences from
The Traveller Book:
Welcome to the universe of Traveller! In the distant future, when humanity has made the leap to the stars, interstellar travel will be as common as international travel is today. Traveller is set against that background drawn from adventure oriented science fiction. The scope and breadth of this game are limited only by the imagination and skill of the players and their referee. Traveller is an entire universe to be explored, where almost any situation which occurs in a science fiction novel, movie, or short story can be recreated with only a little work on the part of the referee.
Traveller postulates that mankind has conquered the stars, and that travel from one stellar system to another is commonplace...
Notice the differences from the Book 1 text. First the idea that star travel is "as common as international travel is today" (which runs counter to the notion of "a large (bordering on the infinite) universe ripe for the adventurer's bold travels" found in Book 1. (At least for me.)
And then a little later we have the phrases "conquered the stars" and that "travel from one stellar system to another is commonplace." When I read these words they run counter to the
spirt of a "universe ripe for the adventurer's bold travels" found in Book 1. (If there is confusion about this please compare the differences between the word "bold" and the word "commonplace.")
It is only
after these sentences we get references to the limited communication comparable to the 18th century.
These passages by themselves are fine if that's the kind of setting one wants. The trick is that the rules don't support these sentiments. The rules (consistent from Books 1-3 in 1977 through
The Traveller Book in 1982) suggest a fairly dangerous life for people who travel between the worlds. There are hijackings, pirates, risky jumps because of limited refined fuel. There is nothing that seems commonplace about space travel at all. Moreover, the Main World generation system, which produces a crazy patchwork of high and low tech worlds and limited starports for refined fuel and starship repair and construction doesn't suggest anything like "conquered the stars." The rules support the more rough and tumble feel of the Book 1 text's introduction where there are great expanses of space between worlds ("bordering on the infinite") that are barely in touch with each other.
A few sentences later in
The Traveller Book we find this passage:
Traveller is a set of detailed rules covering how the universe operates. These rules govern day-to-day activities to be expected for any individual.
There is nothing like this in LBBs 1-3... and I think for good reason. There is are a few rules about "day-to-day actives" (mostly to do what interstellar trade)-- but most rules, the vast majority of them, are about exceptional moments: Encounters with animals, combat situations, combats in space, determining surprise, psionic powers, bribery, putting on vacc suits during an explosive decompression, fabricating "a new main drive bearing as a starship plunges into a flaming sun."
The rules of
Traveller are there for
exceptional moments. And that assumes play is focused on exceptional situations and requires a setting ripe for such exceptional situations.
But the text of
The Traveller Book suggest that the game is about day-to-day activities. And the book delivers on this: One of the adventures included in
The Traveller Book is about endlessly wandering around trying to get some paperwork filled out.
I would offer that this point of view (found in
The Traveller Book but not in the LBBs) runs directly counter to these sentences found on the last page of Book 3 in the 1981 edition:
The players themselves have a burden almost equal to that of the referee: they must move, act, travel in search of their own goals. The typical methods used in life by 20th century Terrans (thrift, dedication, and hard work) do not work in Traveller; instead, travellers must boldly plan and execute daring schemes for the acquisition of wealth and power.
Note that the these sentences make it clear that mundane, "day-to-day" activities "do not work in Traveller." Such activities (thrift, dedication, and hard work) are not what the game is about. It is the exceptional and the adventurous that will persevere. In Books 1-3 the game is about bold plans and executing daring schemes.
I offer that the re-worked text of
The Traveller Book (everything from the text on the first page of the book setting up the vision of play ("day-to-day") the focus on MegaCorporation and other details of the Third Imperium, to the "Exit Visa" adventure) are a sharp contrast to the text quoted above from Book 3.
Traveller as introduced in
The Traveller Book is
not about exceptional situations (after all, interstellar travel is as "common" as international air travel) but is in fact quite mundane in many ways. (The fact that
rule in The Traveller Book often contradict this "day-to-day" point of view is a weirdness -- and I think helped spark lots of debates as people tried to square the setting fluff words they read in
The Traveller Book with rules that did not support that fluff.)
In short, the LBBs offer an open-ended framework for making your own setting with rules that construct implied setting details of a rather rough and tumble setting.
The Traveller Book keeps the rules of an implied rough and tumble setting but surrounds the rules with text that not only introduces a specific setting but a setting that is much more civilized and tamed than the rules would suggest.
Anyway... that's my long answer to your question.