Blackbox Testing: This is always user or client based testing where testing is done based on the requirement provided. This testing is done by testers only.
Whitebox Testing: This is to verify the flow of the code base. Testing the flow of condition statement, loop statement etc. This mainly from developer prospective.
Unit Testing: This is part of white box testing as you test each methods in code with your test data and assert that. Now a days this done by testers and company looks this skill from tester where they are able to understand the code and algorithms.
