Private transportation carries your party exclusively from your hotel door to your next accommodation in each destination. In a private transportation you can decide at what time to be picked up and can stop up to one hour free-of-charge along the way for lunch or something interesting that catches your eye. You can also improvise side trips along the way between destinations (although this might incur in an extra cost). In other words, this is your ride all the way.
A shuttle is a scheduled ride shared with a few other people, and it’s not always door-to-door. Shuttles have set routes they take to pick you up and drop you off, and sometimes that means hopping on a taxi to finish the last couple of blocks to your next hotel. Since shuttles pick up several people in different locations on a set route, the shuttle won’t necessarily be punctual to precision, so you should allow ten to fifteen minutes before or after the scheduled meeting time, and be ready with your voucher and luggage.
The great thing about shuttles is that they’re a lot cheaper than private transportation and a lot faster and more comfortable than public buses.