For me it's a hard yes, at least if we're talking about a world that features both. Even if we ignore the various ways those are portrayed now, there are massive differences in the cultural baggage both from 10-30 years and hundreds of years. Gnomes are generally seen as more magical creatures than dwarves (although not always) and there are legends and fairytales involving them from hundreds of years in the past. Dwarves are a much more recent invention, as they were popularized by western fantasy; although there are some way older sources, they are not well-known and quite similar to how they're seen currently.
Additionally, dwarves are much more commonly associated with a race, unlike gnomes, which are often associated with individuals that do not represent any particular race.
Edit: A funny thing is that what we see today as dwarves and gnomes were often called elves in the past.
Another interesting fact is that, true to legends, the most powerful spirits of earth are often called gnomes (typically with a capital G). That has about as much to do with the common image of a gnome as it has to do with the common image of an elf.