That's absolutely right.

S-expressions are a syntax for data. It's more related to what a tokenizer does, but with nested lists of tokens - not a flat token stream. It's only loosely related to an AST, since the s-expression represents some form of nesting - but not explicitly what kinds.

S-expressions know nothing about the syntax of the program language Lisp (what is the syntax for the LET operator?). If we have a Lisp expression, an AST for it would need to represent specific language constructs - like knowing that LET is a built-in operator and has parts like a list of bindings (where each binding is a symbol or a list of symbol + value form, optionally declarations (with their specific syntax) and a list of body forms. The s-expression does not represent that: in

  (let ((let 'let))
    (list let 'let))

the s-expression does not represent that LET is a built-in operator, a variable name, a symbol, a variable name and a symbol. All we see is five LET symbols and no additional information.

Writing Lisp code using s-expressions allows us to use data manipulation functions both on text and on internal Lisp data: reverse, transpose, move, move in, move out, ...

We can then also enrich the editor (or other tools) to understand the syntax of Lisp. Example: know what the structure of a LET form is and then allow for example to manipulate the binding list, knowing where it is and what a variable and what a value form is.