DATs were well before recordable compact disc players. But there was never any significant (or any at all?) content for DAT commercially, so it would be only for recording vinyl. You couldn’t even record a CD to DAT because of the (breakable) copy protection.
DATs were considered pro pieces, IIRC mostly to record live shows. I had (still have) a DAT and it was fun to play with but you could really only use it as an upgrade from a cassette except you couldn’t buy any content, there were no cars with DAT players, and you couldn’t make mix tapes for others.
DATs were also 16/48 instead of 16/44 like CDs. So there wasn't perfect compatibility in terms of digital dumps in either direction. They were compatible natively with some computer cards. If I recall correctly, the soundblasters were native 16/48.
