TS returns a tree with nodes, you walk the nodes with a visitor pattern. I've experimented with using tree-sitter queries for this, but for now not found this to be easier. Every syntax will have its own CST but it can target a general AST if you will. At the end they can both be represented as s-expressions and but you need rules to go from one flavour of syntax tree to the other.

AST is just CST minus range info and simplified/generalised lexical info (in most cases).