Some people are good at blitz/bullet chess. Others are good at OTB chess. Still others are good at both. You seem to fit the OTB chess category. It's okay to not be good at blitz. If you improve your blitz skills though you can play better and faster on OTB games. I guess you can say they are separate skills if you are used to slow moves where you take your time.
Hope this answers your question.
I suck at blitz chess. My blitz rating is about 600 points worse than my standard rating. If I've learned anything, it's this: when I actually get to think about my moves for a few minutes, I'm pretty decent.
So, this might sound like a weird question, but is it important for me to work on my blitz abilities? Will it help strengthen my regular game? Or are they two separate skill sets?