Gnomes live in the woods, talk to badgers, carve houses into giant mushrooms, and despite being a little eccentric are otherwise okay. Ish. If you can have a normal conversation with a little man or woman and they are not trying dig a hole or cut your head off, it's probably a gnome.
Dwarves are the incel brodude dickholes. They go off into the mountains, spend all their time drinking beer and bulking up by mining and fighting and working out. They grow enormous beards as a sign of
Kobolds are gnomes that went to live deep underground where there are no badgers to talk to, and have gone a little mad as a result. Some paint themselves blue, some wear the skins of lizards or dogs. All are mischievous to some extent. They often run around on all fours, and have developed a weird yelping language that sounds like those irritating yapping dogs your great aunt keeps. What no one realises is that this is a dialect of the language of ghouls.
Redcaps are gnomes that have gone beyond "eccentric" into "completely unhinged". The serial killers of gnomish society, these nutters think that if they murder everything they will live forever, or become all-powerful, or some such nonsense. Tiny Ted Bundy in a fancy hat.
Gnomes will, at a push, acknowledge that dwarves and kobolds are their -- misguided -- kin, but prefer not to talk about redcaps and fob off any claims of similarity. They would say it's a case of convergent evolution if they knew the word. Dwarves, for their part, deny any relation to the -- clearly inferior -- others and often try to eliminate kobold communities. Kobolds don't talk sense long enough to answer the question in any useful way, but do seem friendly enough to the others, if encountered. Good luck getting an answer from a redcap.
All of the varieties of gnome-kind -- even kobolds and redcaps! -- get quite, um, bashful at the mention of leprechauns.