What are the two main types of software testing?

You likely mean two broad types of software testing. Common pairings are:

1. Functional testing

• Verifies what the system does matches requirements.
• Examples: unit testing, integration testing, system testing, user acceptance testing (UAT), API testing.
• Focus: features, inputs/outputs, business rules, UI behavior.

2. Non-functional testing

• Verifies how the system performs rather than what it does.
• Examples: performance/load testing, security testing, usability, reliability, compatibility, scalability, maintainability.
• Focus: speed, stability, security, user experience, resource usage.

If you meant a different "two types" (for example manual vs automated, white-box vs black-box), tell me which pair and I’ll summarize those.