Assuming she's not married, and
assuming she's not a Niddah, then:
Firstly there's an Issur of Yichud, that forbids one to be secluded with a member of the opposite sex to whom one isn't married or closely related like a sister or mother.
If she is a divorcee and he's a Cohen, then there's the sin of Chalal.
I'll use the word sins to refer to an action a verse disapproves of. We're not Gcd's gatekeepers to know the score.
This article (in Hebrew) discusses the issues in depth. Some highlights:
The Rambam says such a person deserves 49 lashes (each time he sleeps with her).
The Tur seems to agree with the Rambam, adding that one (Bet Din, I assume) should force them to separate.
No Get (divorce) is required, as long as no act of Kidushin (in the presence of 2 Kosher witnesses, while stating it's being done for Kidushin) has been done.
- Rambam forbids it unless you're a king.
- Rosh and Tur forbid it because of Nidda issues
- Ramban allows it even for a layman
- Rav Yaakov Emden claims Pilegesh is a good solution for various problems.
- Radvaz emphatically forbids it nowadays.
However, a Pilegesh was a 2nd class wife and not an extramarital relationship (usually hidden from public).
If at any point in time the couple claim to be married, and live together as a family unit, then halachically they are considered married, and she would require a Get - else she's committing adultery if she ever lives with (or marries) anybody else.
Him being married (or not) has no impact on the above, unless you include the sin of not Loving your Wife as Yourself, and being unfaithful definitely would qualify.
No obvious Ashkenazi/Sefardi difference, it seems to me.