Yes, your both statements are valid.
Infinite fleet could pull in any number of vehicles to solve the problem, while finite fleet should work with what you gave it.
Infinite fleet tends to use more vehicles than required, while finite fleet solutions tends to left out jobs - even when there would be solution for all the jobs.
There are technics to drive the solution to use less vehicles. One of the easiest way is to use the fix cost for vehicles, which penaltieses adding additional vehicles to the solution. Also see this related article for some additonal hints!
But an important note, that all these technics only drives the solution toward less vehicle use, they don't ensure to use the lowest number of vehicles.