No, they’re different. ‘Shaping’ is deciding how to combine adjacent characters, mostly by changing their forms as needed, and secondarily by adjusting their horizontal or vertical positions. ‘Layout’ then involves taking those shaped characters and placing them on the page to form words and sentences. There’s some overlap — e.g. you could use shaping to implement the mojikumi rules in section 3.1.2 here — but by and large they’re separate things.

text shaping is not a thing. Unicode provides some basic parameterization (e.g., indicating where valid line breaks can occur in a text), but does not provide much more in the way of layout specification, nor should it. It’s a text encoding specification, not a typography specification. You will also notice that it does not include, e.g., specifications about Latin alphabet typographic ligatures either (e.g., f+f+i → ffi). The existence of some ligatures in the Unicode standard is a sop to backwards compatibility with older encodings only (this is also why Unicode includes superscript/subscript digits, box drawing characters and a number of inconsistencies in how different scripts are managed).