Normal waypoints are just labeled with a number, while named waypoints can be given a name. As far as I know there is no functional difference, this is just a convenience feature.
Rendezvous waypoints can be used with standing or conditional orders. You can probably use it to automate things in a clever way if you can think of one.
Points of Interest are supposed to exist only for a limited time and are automatically removed once visited or if time expires, and can also be used for standing orders, but I'm not certain if this functionality was implemented fully as I've never used them. Supposedly, the "urgent" ones last longer and are also a higher priority for a fleet with standing orders to visit. I think in practice they see very little use since usually player like to investigate such things themselves, but it could be useful for example to have a scout in a survey fleet visit all of the CC2.0 planets in a new system and check for aliens in an automated manner.