Grayshirt - Delay enrollment in college for a year, your eligibility clock starts ticking a year later, end up with an extra year to grow and mature. You can't practice, can't be around the team in an official capacity, obviously can't play, etc. MarQueis Gray was effectively a grayshirt (because of the lovely NCAA), and we were initially recruiting Anyanwu and Lauer as grayshirts, though they were on scholarship right away after plans changed. This is a great way to get a player that you think is small/immature/unrefined and have him start his eligibility when he's 19/20 instead of 18/19, or to secure a commitment from a player you really want but don't have space for in your current recruiting class.
Blueshirt - Enroll in college right away as a preferred walk-on with a wink, wink, nudge, nudge promise of a scholarship as soon as feasible, i.e. the following semester or following school year. This is for a guy you want to be with the team and practicing right away (can play if needed) but just don't have a scholarship available to give. Another wrinkle is that the player may not have been recruited in any way prior to joining the team.