'type' is for types, and 'assume' is for properties. In Maple, there used to be only types at one point, so the question "what is a type" was never really asked.

But in retrospect, the vast majority of types in Maple are ``syntactic'', in other words, they test something about the representation of an object. Of course, since types can be arbitrary computations in Maple, some are also semantic (like checking that an integer is prime). But the core types are syntactic, especially the so-called "structured types", which are really the work-horses of the dynamic type system of Maple.

Properties on the other hand are most definitely semantic. This is why one can assume that certain symbols have certain properties. 'is' then checks those properties, so in effect is a mini-automated-theorem-prover embedded in Maple (but as a pure black box).

One design decision was that all types were to be properties too. This is both really useful and (in hindsight) a serious mistake. To have both syntax and semantics together is very dangerous -- and doing this badly is the source of many of the paradoxes in logic, and incidentally includes Frege's original mistake in his logic (ie the Russel Paradox). It is not impossible to get a consistent logic that deals with both syntax and semantics, but it is remarkably hard to do so -- see Chiron: a multi-paradigm logic for one example.

As Robert Israel pointed out, a lot of types are not in fact known to assume, so 'is' cannot reason about them at all. So one needs to be careful to only use those names which are actually known to assume -- a set which is actually not documented! Just to make things more interesting, the type-formation operators (like and, or, not) are different from the property operators (And, Or, Non). Furthermore, the type logic is 2-valued [FAIL is not allowed in types] and the property logic is 3-valued!