(define-method (equal? (a <string>) (b <string>)) ...)
on the other hand, means that you want to *extend* the current behavior of equal? with a specialization to two strings. The method is then added to equal?, which in guile-1.8 was from scratch a "primitive-generic".
Actually, this is misguided. I should have examined this problem more carefully, and also read your later emails more carefully.
You see, I was under the impression that primitive-generic capability had been removed for equal?. It has not. It's only the printed representation which has changed.
Your bug report contains two problems. One concerns why define-generic doesn't create a new generic. I believe this is an intentional or unintentional change at some version. The other problem concerns the dispatch rules for primitive generics.
You are right that the dispatch rules are special for primitive generics. The purpose of primitive generics is to get around any performance penalty for standard behavior, so primitive generics first try standard dispatch. Then, if that fails, GOOPS method dispatch is used. The standard behavior of equal? is to simply return #t when applied to a single argument regardless of type. This is the explanation why you get #t for (equal? <foo>).
One way to view this is that the dispatch of primitive-generics is partially constrained.