Lifter, tappet, bucket, etc..
Somehow the camshaft has to make the valves move up and down. The cam does not act directly on the valves, but has some sort of mechanism to go through.
Some engines use tappets and pushrods with a rocker arm [like old V8s]. Some use a bucket only [common on overhead cam engines]
The term 'Lifter' probably came from old flat head engines, where the cam would push on the tappet and 'lift' it , then it would lift the valve.