Same, but "pad" has a trendy, hip, cool feel to it. The origin of this use of "pad" probably is the fact that a mattress can be thought of a pad upon which you sleep. Hence, "pad" came to mean "home" because home is where you sleep.

I don't believe there's any difference. "Bachelor" in this context means "unmarried man." "Apartment" is plain language, "pad" is slang. (One dictionary calls it "slang," another calls it "informal, for a person's home.") A "bachelor pad" simply means one that is set up the way a bachelor might set it up; suitable for entertaining a romantic visitor, for example. (I wonder if it's still current? It has a 1960s-1980s feeling to me.)

Hi Jung Kook, Bachelor's apartment is smaller than a studio. It refers to physical space. Bachelor pad refers to a place where it is assumed a single person will live. It can be small or it can also be large, flashy or expensive. For example, Brad Pitt lived in a swanky bachelor pad. We aren't going to think Brad Pitt lived in a tiny place smaller than a studio, but we will think that was a place where he lived when he was single!