You are partially right on both accounts. The distinction between recoilless rifles is only significant when we're talking history an nomenclature, and speaking about dedicated crew-served weapons that were traditionally called recoilless rifles (безоткатное орудие) and nothing else. And these ones are obsolete.

On the other hand, for example, the essential RPG - RPG-7 - expends all its propellant in the tube. Does it make this so-called rocket launcher a recolless rifle? Doesn't matter, especially since the term "rocket-propelled grenade" is a backronym, and RPG means hand-held antitank grenade. We could continue, but it becomes increasingly pointless.

Moreover, you're grossly oversimplifying the matter of recoil. Not that we need it to be more complex, BUT you tried to ELI5 it with the weirdest explanation I've ever heard, and continue to elaborate on it at length.

Meanwhile, felt recoil is the force that the expanding gases in the cartridge exert on the walls and bottom of the cartridge case (and, it many cases, on the gas piston further down the barrel). THAT'S ALL. Where that force goes further is the matter of firearm's construction. It might compress springs and move metal bits, yes - and the manner of how heavy the bits are and how they move sometimes inform the character of the recoil.

But to call the spring a REASON for feeling recoil is ridiculous. Most of the firearms people used for the last 100 years did not have any recoil springs, and translated recoil to the shoulder completely rigidly - like, say, all bolt-action rifles and all revolvers.

I'm frankly at a loss of words, because you have such an impression of your own competence in the matter I don't have any idea how deep I need to go to ELI5 it here.