A Jack Handplane is a middle size “bench plane” (i.e. planes that are used so often that they are usually on your workbench). If you’re on a budget a jack plane can temporarily be used in place of other planes that perform specialized functions: (1) rough stock removal (if you buy a second iron/blade and shape it with a curved “camber”), (2) jointing board edges (as long as they aren’t too long), and (3) smoothing the boards.
Thickness planer. A thickness planer is used to fix surfaces of imperfect wood. If you are picking up less than perfect wood from the lumberyard, wood with some surface defects, a planer will let you fix that wood in the quickest time. A thickness planer pays for itself quick as it allows you to buy cheaper wood that doesn’t have perfect surfaces and fix it yourself. Be careful though. You loose wood during planing. So the remaining amount of wood still has to be worth the price you paid for it.