amoeba (as a taxonomic group); Amoebozoa
Refers to the amoeba as a biological group (Amoebozoa), not a single organism. The common word for an individual amoeba is アメーバ.
Amoebozoa is a group of single-celled organisms that move using pseudopods.
アメーバ is the common word for an individual amoeba, while 変形虫類 is the formal taxonomic term for the group Amoebozoa.
Compound of 変形 (henkei, 'transformation') + 虫 (chū, 'worm, insect') + 類 (rui, 'kind, group'), referring to the shape-changing nature of amoebas. The exact historical derivation is uncertain.