There are several types. You could use different ways to classify them. One way is to classify them by type of work done. Some of those are for production, quality check (QA/QC) on the production process and on the in and outgoing materials (e.g. oil and gas, food, plastic).
Research and development (R&D) laboratories. These are for doing basic research or product development. This can range from physics to chemical to medical
Medical or Clinical laboratories. Mostly found in hospitals and clinics or pharmaceutical companies.
Biosafety Laboratories. Focused on working with bacteria and viruses, they can be classified as ML-I, ML-II and ML-III, BSL-3 and BSL-4
And you also could name Clean Rooms. Special environments with the focus on minimizing pollution/contamination.