Masking tape is different from painter's tape. Painter's tape is meant to be put down on a 'surface' and not leave any residue nor absorbe paint. Masking tape, on the other hand, does BOTH the aforementioned, and is primarily used in the art / graphics business for the exact purpose of masking something out.
Go to any home center or hardware store and ask for Painter's Tape. If you're shown a roll, look for it to say on it that it's used for 'masking' when painting. 3M makes a painter's tape and on the INSIDE of the roll you'll see Painter's Tape in 3 languages! (Or something like that. Just look for the English wording.) 3M's Masking Tape says Masking Tape on the inside of the roll. In either case, you don't have to open the package up to tell which it is. Again, just read the inside (that's inside the 'hole') of the roll.
And lastly, always take your time when you peal off the tape. Personally, I'd wait until the paint dries. If it's still wet when you remove the tape, it may 'run' on you. Painter's tape is best removed when the paint is dry. Remember, it doesn't absorbe the paint, hence, it won't peal the paint away. My best to ya and hope this helps.