Why `X=1,X=1.` prints `X=1` instead of `true`

There are no assignments or equality tests in your query, only unification of terms. The query succeeds by unifying the variable X with 1 and that's what the top-level reports: it tells which variable bindings makes the query true.

After the first goal in the conjunction, X = 1, succeeds, the second goal is the unification 1 = 1, which trivially succeeds.

P.S. Also note that Prolog systems differ in the way they report successful queries. Some print true, others print yes (the traditional way that successful queries are reported).

When the answer is true and a value is bound to variable at the top level, the value of the variable is displayed, which implies the result was true.

Here are some examples.

test_01 :-
    X = 1,
    X = 1.

test_02 :-
    X = 1,
    X = 2.

test_03(X) :-
    X = 1,
    X = 1.

test_04(X) :-
    X = 1,
    X = 2.

and when the examples are run from the top level using SWI-Prolog

?- test_01.
true.

?- test_02.
false.

?- test_03(X).
X = 1.

?- test_04(X).
false.

Here are some examples that are done only in the top level

?- X=1.
X = 1.

?- 1=1.
true.

?- 1=0.
false.

?- 1==0.
false.

The first X=1 in my command is an assignment, and the second one will be a check of equality.

X=1 is not an assignment it is a unification of the integer 1 to the variable X. The second X=1 is not a check of the equality, it is another unification of X to 1, but since X is bound to 1 by this time, it is really a different unification.

To do equality checking in Prolog use ==, e.g.

?- 1 == 1.
true.

?- 1 == 2.
false.

Also , is the logical and, so if

?- X = 1.
X = 1.

then 1 is bound to X and is true and similar for the second line in your question.

However the code has to be also viewed as

?- true,true.
true.

as opposed to

?- true,false.
false.

While ; is logical or

?- true;true.
true ;
true.

?- true;false.
true ;
false.

?- true;false;true.
true ;
true.

?- false;true.
true.

?-  false;false.
false.

Notice that the first 3 answers have 2 results, but the last two answers have 1 result.