I confused those features of the native language server, so here's the summary:

  - Go-to-Definition: For variables, jump to the declaration. For functions/classes/types, jump to its types or implementation.
  - Go-to-Type-Definition: For variables, jump to its type declaration instead of the variable declaration.
  - Go-to-Implementation: For interfaces/abstruct classes, jump to (multiple) implementations of the method. For compiled TypeScript file (like them under node_modules), jump to its implementation rather than .d.ts files.