Hug me - a brief embrace, like hugging a friend.

Hold me - more romantic, you only would say this to a boyfriend/girlfriend or someone you are romantically involved with, or a child might ask a parent to hold them/pick them up. It would be very weird for an adult to say it to someone they aren't dating or married to.

@ Kate (Y)

I'm so very confused.
You can meet please?

Could you please meet with me?
or 
Could we meet please?