The governing distinction
Two processing models, and why the answer differs
A single privacy answer for this site would be false, because the tools don't share a processing model. One set computes results in the browser from code delivered with the page. The other calls a language model, which can't happen locally, so the text has to travel.
Every tool page states which model applies before you paste anything, and a run allowance is the reliable tell: it exists to meter server cost, so a tool with one sends text, and a tool without one computes locally.
This page takes each model in turn, then two things that apply site-wide regardless of which tool you open: analytics, and the providers the service runs on.