Grove shields are meant to use the Grove system of sensors, that all use a common 4 wire plug. I believe Grove was created by seeedstudio, and you can read more about it here:
http://www.seeedstudio.com/wiki/GROVE_System. The advantage of the grove system is it is plug and play and needs no soldering in the original Grove system. However with the digispark, I believe you will need to do a little soldering to make the Grove shield itself.
A boost shield is meant to take a battery which is less than 5 volts and use voltage converters to increase the voltage to 5 volts so that the digispark can run. Example batteries include 2 AA batteries that provide up to 3 volts (alkaline) or 2.4 volts (Nimh rechargeable) or many common LiPo batteries which run at 3.7 volts.
I believe the MOSFET shield is a little like a boost shield in reverse, and it would allow you to control higher voltage devices from the digispark. You might be able to use MOSFETs to drive motors, but if you want to control a motor, you should get a motor shield, unless you want to do all of the programming to control the motor.
I should mention besides normal motors, there is a variant called servos that are controlled differently. A motor spins in one direction or another, and you have to tell it when to stop, and what direction/speed to use. A servo is setup to move between 0 and some limit (usually 180) degrees, and you just tell which position to move to. For many robotic controls, a servo is better than a more general motor. You would not use the motor shield to control the servo, but instead no shield, the through the hole shield, or one of the breakout shields (I forget which breakout shield is wired for servos).