Is there a difference between the strong nuclear force, and the strong force (without the nuclear in between)? I have heard that the strong nuclear force binds protons and neutrons together, while the strong force binds the gluons together inside protons and neutrons. Is that true?
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At a fundamental level, there is only one strong force, which is mediated between gluons between quarks and gluons with non-zero color charges.
In practice, due to confinement, at large distances (or equivalently, low energies) compared to the confinement scale, there are are no objects with a net-color charge. Loosely speaking, this scale is some fraction of the size of a nucleon.
Therefore, inside a nucleon, free quarks and gluons directly interact via the color force.
Nucleons can also interact. In the low energy effective field theory description of nucleons, the relevant degrees of freedom are nucleons and pions, which are color-neutral objects. Nucleons attract each other by exchanging pions.
However, the ultimate, fundamental origin of these nucleon-pion interactions is the same strong force that binds quarks and gluons. The effective low energy description is a convenient way of describing a process that, in more fundamental terms, would involve many complicated interactions of quarks and gluons inside the nucleons.
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1$\begingroup$ Forgive me if @Andrew actually mentioned this in the text: the latter effect, where nucleons are held together by interactions mediated by pions, is called the "strong nuclear force". Note that in addition to what Andrew said, pions are also integer-spin particles, so they're bosons, and thus candidates to carry force -- even though they're composite particles. Somewhere in the Land of YouTube, there's at least one video showing -- without any math at all, but with pretty graphics -- how the strong nuclear force looks like an independent force but is really the strong force underneath. $\endgroup$ Commented Aug 12, 2023 at 23:26
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$\begingroup$ Thanks for the additional information, @TimWescott! $\endgroup$– AndrewCommented Aug 12, 2023 at 23:26