A parasite is an organism that lives on or inside other organisms (host) and draws nutrition at the expense of its host.
Amoeba proteus is a free-living organism and capable of independent existence. While Plasmodium vivax, Trypanosoma gambiense and Entamoeba histolytica are parasitic protozoans.
Plasmodium vivax causes malaria. The causative agent of sleeping sickness is Trypanosoma gambiense and of dysentry is Entamoeba histolytica.