Or you pass your intelligence check & realize that they really were talking about different races.
Elf, dwarf, human, etc - they really are different races.
Sure, within an individual race they also have ethnicities & heritages (wood elf, drow, assorted human cultures in GH/FR & whatever else). But that doesn't stop there from being 5+ actual races to choose to make your character from.
Technically, they're different
species though there's a question about fantasy and cross-breeding here especially considering that the standard lore is that Orcs, Elves and Dwarves are all creations of gods, while humans are...evolved I guess? (or created by the original evil incarnation of Pelor) And that none of them have any shared genealogical history. They're all flesh and apparently that's good enough?
A race can exist within a species. IE: Drow and High Elves, they are physiologically quite different, but there is little true biological difference (skin color, hair pigmentation, the size of the women) all of which can be achieved through selective breeding (which the Drow practice). The Drow are also a an ethnicity because they have a fairly unique culture, but there could be multiple ethnicity of Drow without any biological variation.
It really depends on what you want to achieve with the term "race".
If we're talking about different biological creatures, then the technically correct term is "species", but that's fairly sciency for D&D.
If we're talking about different physical appearances but little biological differences "race" (as the older usage) is applicable, while "ethnicity" is more modern (and reads like it too).
If we're talking about people who generally look the same an ascribe to the same system of beliefs values, then culture is applicable here, but "ethnicity" also works, though "nationality" is the more modern usage (yes, even for groups of people who do not have nation-states). Heritage can also work, but heritage is not inherently specific to biology or culture. Ancestry is much the same as heritage, though leans more towards the biological than the cultural, but is often used interchangably.
If we're talking about people who behave the same way, but may not be biologically the same, then the term is "culture".
Since D&D differentiates "races" by giving each of them specific physical depictions and physical/mental stats, the most appropriate word in this context is "species". The older usage of "race" would be more applicable between the D&D differences between say, High, Wood and Dark Elves(Drow). They're the same species, but have noticeable (but what would be considered biologically minor) variations.
D&D's biggest problem and confusion with terms comes from the fact that both elves and orcs can cross-breed with humans. It's unclear if orcs can breed with elves, and there is history that dwarves and elves can cross-breed, but there's not much info on if an elf and a dwarf can cross breed.
If we were to remove the ability to cross-breed, the terms would fall into place nicely, species would refer to Elf, Human, Orc, and race or ethnicity would refer to High Elf, Brown Orc, Mountain Dwarf, etc... Culture and nationality would then be left up to the table. Ancestry and Heritage would only be appropriate when referencing who your forebears were and who a character identifies with (ie: a Human raised by Orcs may consider Orc-dom his Heritage, but his Ancestry humanity).
I'm sure I didn't need to write all this but really, it comes down to the problem of species with no shared biological history being able to cross-breed that makes D&D's terminology problematic. That can be resolved by removing the ability, or writing in shared ancestry, ie: Humans who migrated thousands of years ago to the Feywild became the first fey, or fey who were banished from the Feywild devolved into humans, and the Orcus?Grummush? got jealous and kidnapped some humans and turned them into Orcs. Moradin was just lazy and stole some orcs and made their hairier, and that's why Orcs and Dwarves hate each other.
Anywho.....
