I feel like I am becoming quite disagreeable. I think the dead horse is that very few programmers use the term 'contract' and in my experience either they use it in the sense of 'design by contract' or they are just making things up. Honestly, there is nothing legally binding when programmers agree to an interface or behavior. The word is marketing-speak from some company. Words like specification or even the word interface itself are better. The word interface implies an agreement.
I don't not agree.

That is, I agree.
Again, 'interface contract' is just silly. An interface specifies and requires exactly what it says it does -- the point where two things meet
It does sound redundant, so one or the other would suffice whereas both might cause confusion, yes.
Agreed. But an interface is only part of a specification. If you have a method called save() that doesn't save then it may have the proper interface, but who cares at that point. Honestly, interfaces are the simplest part of the spec to enforce. When they are wrong it is usually pretty clear even without error messages. And once they are right they usually stay right. PHP interfaces help a little in catching these trivial errors.
An interface, in the most generic sense, I would consider the most important part (and difficult to get right) of software development. A PHP interface, which is what I think we are discussing, is relatively moot in importance, yes. I find it rare where I need an interface, and an ABC would do what I need.
I think they are relics of a complied era, when products would ship with a library file or DLL and the authors would distribute C/C++ header files or interfaces to allow extension developers to build new plugin modules while enforcing compatibility in method sigature, etc.
At the very least I suppose, what an interface does do, is offer a minor documentation to extension developers ho wish to replace parts of your system, if it is build extensible in the first place. When a class that implements an interface does so to the point where the compiler stops b*tching you have complied with the interface, which is half the battle. Now how or whether you implement the behavior is another battle.
Cheers,
Alex