What is the differences and similarities between refinement type and liquid types?
They are, to a first approximation, the same thing. "Liquid types" come from LiquidHaskell (1, 2), which is a programming language and verification framework based on refinement types. The Scala repository that you link to is an implementation of refinement types for Scala.

In terms of programming language theory, refinement types is the technically correct and more general term. LiquidHaskell and the Scala repository are examples of implementations of refinement types.