Distinction without a difference. If you can't explain to your students why the words out of your mouth are useful, you've already lost them.
The fact of the matter is that you're getting hung up on implementation details that do nothing to explain the concept.
Pointer arithmetic, how pointers interact with the type system... those are important, but they're completely incidental. There's no fundamental reason C had to implement pointers that way. They're factoids about how pointers work in C, practical mechanics. They tell you nothing about what pointers are in essence: a memory address.
And I don't know if you've worked with novice programmers lately, but it seems pretty obvious to me - based on how so many people get their heads discombobulated about pointers - that that conceptual clarity is needed. The details you're listing don't need to be in the first sentence.
That C pointers have a type which is used for checking, semantics of memory access and arithmetic falls into a category that I like to call requirements, whereas I use the word implementation detail for something like how many bits are in a pointer, and do pointers to bytes have the same representation as pointers to wider types. (These are also requirements, but ones an implementation can vary.)
I accept your terminology, though. Let the key features of C be called "implementation details". Then, if the goal is to teach C, it is "implementation details" we must teach.
(In any case, the students are probably eager to learn implementation details in the regular sense also, otherwise they would have been satisfied with their Python or Javascript class.)
If what you really mean is that we should teach C by instead teaching the architecture of a machine, whereby C is treated as just a notation for manipulating that machine, and concepts like the type system are considered annoying/distracting details in that notation, then I strongly disagree. Even if it is easier to teach that way, and the students eagerly absorb and regurgitate the simplified misconceptions, they are ill served.
The fact of the matter is that you're getting hung up on implementation details that do nothing to explain the concept.
Pointer arithmetic, how pointers interact with the type system... those are important, but they're completely incidental. There's no fundamental reason C had to implement pointers that way. They're factoids about how pointers work in C, practical mechanics. They tell you nothing about what pointers are in essence: a memory address.
And I don't know if you've worked with novice programmers lately, but it seems pretty obvious to me - based on how so many people get their heads discombobulated about pointers - that that conceptual clarity is needed. The details you're listing don't need to be in the first sentence.