Thank you for this question! Finally someone who might understand that “nanobot” is basically a popular buzzword that has little to no real meaning!
I guess people have idea of nanobots as small robots moving individual molecules/atoms. This idea has been popularized by some sci-fi books, movies, shows.
The idea of “nanobot” is based on the fact that we have seen molecular devices being used in cells (how some things are operated in unicellulars, like “flagelum”). We realized that some molecules offer “moves” conformation upon charge redistribution, upon illumination… So that we know that we can make moving parts on molecular level.
But of course sci-fi authors took this idea and forgot about details. Like quantum mechanics, like thermodynamics…
So…
Nanoparticle is a small piece of “normal” material. An atom/molecule has some properties. That average if you have huge quantity of that material. (An silicon atom has different properties then silicon chunk.) Sure, you must now get the idea that if you have two atoms, they will behave similar to one. Three atoms might start to show more differences… And there must be some “grey” area where you have no more behaviour typical for individual atoms, but you have not yet the behaviour of huge chunk. That is the realm of nanoparticles.
Thanks to this they allow us to have materials and properties based on those effects that emerge only at the boundary of molecules and bulk.
A protein… is basically a nanobot. If we ever produce nanobots they will be quite similar in a lot of things to how proteins, RNA, DNA things work. The similarity will be about the same as knives are similar to claws or teeth. One is natural thing, the other is man made, but for the same purpose. but both need to deal with the same problems.