The terms "Bat Speed" and "Exit Speed" are almost always confused
Bat speed is not the same as exit speed. The two terms are usually confused.
Bat speed is the speed the bat is moving: bat speed is only one indicator of performance that may result in increased exit speed.
Exit speed is the speed the ball is moving as it comes off the bat: exit speed (aka, batted ball speed, speed off the bat) is the ultimate goal in hitting. This is a measurement of the speed of the ball as it comes off the bat. This is the result of at least five factors: bat speed (at contact - may not be max) + pitch speed (at plate - not max), adjusted by impact point on the bat ("sweet spot"), bat composition (ex. BESR rating), and ball composition (ex. COR rating).
Charts showing reported bat speeds and exit speeds (there are all from 3rd party reports):
Warning: In some of these reports, it is unclear whether they used non-wood or wood bats, and whether they used a pitched ball, or a tee.