Handsfree just mean that the flange for suction doesn’t need to be held in place by hand or with bra. This is for preference of user as there are bras and other ways to hook the flanges if you want. The shape is also less obvious if you want to pump in public.
Manual / machine is the method to pump. Manual meaning you pump with your hand or using vacuum. Usually recommended if you latch your LO but want to pump more than enough to maintain supply or keep a stash.
Machine pump means completely pump milk without needing hands to press. Usually recommended when your LO is not latching at that time, eg when you are at office.
I have only tried the Spectra S1+ pump and found it very good as my LO didn’t latch at all.