What are the differences between InheritsFrom and the is operator?

Yes, there is a difference. InheritsFrom is class function and it's primary purpose is testing whether class IS (inherits from some class).

You cannot use is operator on classes.

TMyChildClass is TMyClass would not compile, but you can use TMyChildClass.InheritsFrom(TMyClass) instead.

The is operator is built on top of InheritsFrom. So,

obj is TSomeClass

is implemented as

(obj <> nil) and obj.InheritsFrom(TSomeClass)

The expression obj.InheritsFrom(TSomeClass) is perhaps a little confusing because it looks like InheritsFrom is an instance method. In fact InheritsFrom is a class method, and the runtime class of obj is passed to InheritsFrom as the Self pointer.

So fundamentally is and InheritsFrom perform the same task, at least when restricting attention to classes. Note that is is more general and can also be used with interfaces, for example.

There are obvious syntactical differences. Namely that is requires an instance, whereas InheritsFrom is a class function. Although, as we have seen, the Delphi language does support calling class functions on instance references. And the other obvious difference is that is has a built-in test for a nil reference.

These are just syntactical differences though, the fundamental operation is the same, as evidenced by the fact that is calls InheritsFrom.