Without any other context they both imply that the listener and the speaker are included. 1) Do you feel like going shopping (with me)? 2) Do you feel like watching a movie (with me)? But the context could change the meaning. 1) (he says) I'm going to get a haircut. (She answers) Well I don't want to sit here and wait while you do that. (he responds) Do you feel like going shopping? (implies that she should go shopping while I get my hair cut) 2) DAD, I'm sooooo bored. (he answers) Do you feel like watching a movie? (implies the kid should watch a movie and leave his dad in peace)