The two are definitely not equivalent, but they overlap. Types can replace tests - if an edge case exists but I can define it out of existence with my type sys

The two are definitely not equivalent, but they overlap. Types can replace tests - if an edge case exists but I can define it out of existence with my type system, then I no longer need tests for that case. And likewise, tests can replace types - I can use dependent type systems to define invariants in my system but at a certain point it becomes so unwieldy that it's easier to use tests to define those invariants less formally. In the end, they're just two different tools that both serve the overall aim of software correctness. Demonstrating correctness with one tool may be easier but less thorough, or more complicated but more precise, or whatever else. In this context, if you can get the type system to help you, you'll be able to get away with a lot fewer tests because you don't need to test things like "does this function call a method that actually exists?" or "what happens when this function is passed bad data?".