Morpheus

They literally operate in different worlds. Hard to separate the characters from their milieus.

The only thing they have in common is the name.

Now my question is, was Dream already in DC from the start, or was he transferred from Vertigo Comics to DC comics?

Sandman #1 came out in 1989. Vertigo did not exist until 1993. So he was DC from the start and then transferred to Vertigo.

Gaiman is fantastic and all, but Sandman Mystery Theater is one of my favorite takes of all time on the pulp hero genre, so I'll go with Wes Dodds.