There are multiple assignment types that can be used in Canvas.

Regular Canvas assignments, course Group assignments, Peer Review, Turnitin, VoiceThread

Note - grade center categories are called groups in canvas, so if you're looking to create a Group Assignment you need to look for "Course Group" not assignment group.

Please see the links below for more information on creation, grading, etc. of assignments:

Assignments https://community.canvaslms.com/docs/DOC-4131#jive_content_id_Assignments

VoiceThread assignments https://voicethread.com/howto/canvas/