Black box: Network access without NAC access, and nothing else, external attacker POV
Grey box: Employee who doesn’t work in the IT department.
White box: Full access to all systems, configs, build documents etc. source code if web apps are in scope

Other types of assessments:

Adapted from: https://purplesec.us/wp-content/uploads/2019/07/8-steps-to-performing-a-network-vulnerability-assessment-infographic.png