> Type inference is usually reserved for more general algorithms that can inspect not only how a variable is initialized, but how the variable used, such as what functions it's passed into, etc...

In a modern context, both would be called "type inference" because unidirectional type inference is quite a bit more common now than the bidirectional kind, given that many major languages adopted it.

If you want to specify constraint-based type inference then you can say global HM (e.g. Haskell), local HM (e.g. Rust), or just bidirectional type inference.