While all are a type of rideshare, vanpool is more formal and usually arranged through a transit authority. Vanpoolers pay their fare to the transit authority, and the transit-owned van is used, which includes maintenance, licensing and insurance.
If you ride the bus, train or bike to a transit station, a vanshare can help you complete the ride to home, school or work. Limited to shorter distances than vanpools, vanshares get you the “last mile” of your commute. Just like a vanpool, the vans are operated by the transit authority, require a minimum of three people, and are paid for on a monthly basis. You can check with your transit authority to see the vanshare options available.
A carpool can be informally arranged between two or more people who share a similar commute route. In a carpool, passengers pay the driver an agreed fare to fairly split gas, parking, maintenance, insurance, etc. or carpool members rotate driving their personal vehicle equally.