The "warp core" on a ship is just the power plant. The nacelles under the saucer house the "field coil" machinery that generates a warp field.
Yes, this is gobbledygook. But no moreso than regular "subspace" or anything else in Trek.
For power (ed: including their standard warp drive), the Discovery still has a plain old M/AM reactor. And yes, I did just use the phrase "plain old M/AM reactor" hah
So using "STD" has turned into kind of a unsavory gatekeepy dogwhistle. It tends to bring out the worst types of stereotypical toxic fandom. /r/DaystromInstitute even automod-bans it for that reason.
https://en.m.wikipedia.org/wiki/Project_Orion_(nuclear_propu...
Picturing this in my head was certainly a treat :)
In TNG, they don't practically behave much differently from the warp core, but some of the video game spin-offs had fun with the idea, having destroyed Romulan warbirds collapse into their own engine core, which then evaporated because it was unstable outside of the confines of the gravitational field.