As far as I can tell, any Elisp if-form that is also a valid Common Lisp if-form has the same semantics; but Elisp allows more than one else-form in its syntax, with additional semantics.

It's something like:

  (defmacro elisp-if (expr then &rest elses)
    `(cond (,expr ,then) (t ,@elses)))

Whereas the regular if is like:

  (defmacro cl-if (expr then &optional else)
    `(cond (,expr ,then) (t ,else)))

In a book that uses Common Lisp, you shouldn't see an if-form that isn't Elisp-compatible.