Be careful about terminology. You wrote, "I think, `evalb` is used to compare numbers and `is` used to compare expression, logic. Is this true?" That sentence is not precise, in Maple terminology, and that can lead to misunderstanding here.
Think instead in terms of technical Maple terminology, for example whether something is of type numeric. That includes floating-point numbers, integers, and fractions (rationals, with integers in numerator and denominator). That does not include exact representations such as sqrt(2). Yes, that denotes a "number" in the common mathematical sense, but it is not of type numeric to Maple. A related and useful class is things of type realcons, which would produce something of type numeric if evalf were applied.
The evalb command can compare equality and inequality relations of items that are both of type numeric. It can also test whether two structues are identically the same, by which I mean that they have the same address in memory.
So you cannot generally, reliably compare two expressions (of type algebraic but not numeric) with the evalb command unless you can put both into a canonical form, in which case they are uniquified and the canonical forms are identically the same.
f := x + 1 = (x^2 - 1)/(x - 1);
can be simplified (using simplify or normal, for example) so that lhs and rhs of that normal form are in fact the very same expression. That is why evalb(simplify(f)) returns true.
But not all expressions can be easily put by Maple into some canonical form. (For example, there are mathematically equivalent formulations for some expressions involving trig and special function calls for which a choice of canonical reformulation is not obvious.) That's one advantage of using is, as it has a variety of mathematical operations it can do for comparison.
Another significant advantage of the is command is that it can (often) utilize assumptions on names in symbolic expressions.
Here are some tips:
1) For mathematical testing of an equation (ie. A=B), it can sometimes help is by querying is(A-B=0) since (while zero-testing is hard) at least the target form is clear: zero.
2) In general the is command performs more strongly that simplify (or its friends, normal, radnormal, shake, evalc, rationalize, combine, and expand) alone. It is rare that it helps to make a call such as is(simplify(A-B)=0) , but examples do exist.
3) For inequality testing involving expressions of type realcons you may generally be better off invoking the is command, rather than applying evalf and risking a mistake due to close roundoff error. Like most "rules", this too has its exceptions.
4) If you are going to use the is comand then you might have to write your code so that it handles the case that is returns FAIL instead of true or false.
5) For verification of floating-point results from a computation against a target value you might look at the testfloat command, or the verify command with a float comparator.
6) For verification of data structures (lists, sets, Vectors, etc) you could also look at a call of the verify command, according to the type of the structures' members.
It's a large topic, and a textbook on Maple could be written while covering it comprehensively.
Background reading, Help pages for Topics:
- evalr, shake
- type numeric, realcons, algebraic
- evalc, radnormal, evala, normal