The other meaning of type is the pure, declarative one. Here, variables do not belong to the valid types. In that context, atomic_si/1 and the other predicates fit in. Here, commutativity (modulo errors) holds. And thus alternative search procedures may be used.
(There is a third meaning similar to the second, but it is only standard related.)
Regarding pure, declarative types those again are extra-logical and so, in the context of a first-order logic language, they are arbitrary and conventional. You can say "it's better this way", someone else can say "no, it's better this other way" but in the end of the day there's nothing set in stone. Far as I can tell.
Anyway I really think all those little complaints about Prolog's lack of absolute, pure perfection are always bordering on nitpicky- and from the wrong side of the border, at that. Peter Norvig says Prolog is not a general purpose relational solver, but it's a general purpose programming language. Well, yes, because it was, from the start, designed to be a general purpose programming language! That is, a language that can be used for, you know, actual programming in first order logic. Of course it's not perfect. That has always created a rift in the community, with some people taking the issue more seriously than others. Some have always been happy that they (we) have a language that's 90% of the way to pure, declarative perfection and that lets you express yourself in code in ways that would be really painful in any other language (just think of DCGs vs. the pain that compiler writing is in anything else). Others are always unhappy because they're missing that idealistic 10% that remains on the road to clean and pure declarative perfection. Well, we're not in a pure world. We don't have perfect computers. In fact, our computers just suck. We have to accept compromises, if we want to get anything done. Prolog is almost perfectly balanced in between shitty languages that abuse imperfections in computer architectures and mathematical purity. Personally, I'm grateful to Colmerauer and Kowalski for creating it. I can only imagine the mess I'd make of it if I had to do it myself.