I shouldn't have to, because it is pretty clear to everyone - including you as you just demonstrated - what I mean by - "Some mechanical approaches to the problem of balancing spell-casters and martials is to simply give the non-spellcasters their own spells." The only people who have a problem with that description are deliberately being obtuse so that they can "score a point" rather than have any sort of legitimate discussion.
So yes, technically, often when I say "spells" I am using this as a short-hand for "spell-like mechanics" but out here in the meta where we are discussing mechanics that isn't much of a distinction.
The only people who are confused are people who have a vested emotional interest in pretending to be confused by this for whatever reason.
It's a real distinction for many not some rhetorical ploy. It's the reason some people aren't satisfied with say the Eldrich Knight but like the 4e Fighter both of which use limited use powers with some narrative control (although arguably much less for the 4e Fighter). One uses spells and one uses "abilities that use mechanics that have been traditionally reserved for spells in D&D, particularly limited use in exchange for power and narrative control".
I also pointed out how further divorcing player and character resources might be a better method to model martial prowess than one to one player /character resources given that "magic" can't do the bending fiction for the martial if that bending is needed -- it needs to happen outside the character, which is different than how most spellcasting works but shares some mechanics.
Look, I don't necessarily want to see a martial that uses the exact same structure and mechanics as a Wizard but I also don't want to cross off mechanics just because they have traditionally been only used for spells in D&D. Even if you do use the same structure (4e did), the permission base led to different powers. 4e Fighters couldn't teleport or create elemental damage from nothing.
Anyway, I'm not going to try to persuade you further. No point.
My whole point, however, was to point out that in your mostly excellant earlier post if you were trying to capture the full spectrum of why people have different ideas of how the fighter should be improved and what tools are available to improve it, you should include this perspective as it's one that causes people to butt heads.
If the design parameters are "no spells allowed" then some people will advance the 4e Fighter as a good start. If the parameters are " no abilities that use mechanics that have been traditionally reserved for spells in D&D, particularly limited use in exchange for power and narrative control" then the 4e Fighter is off the table.
Since some people see this difference, I'm not sure why we wouldn't want to be clearer on which design space we are talking about?