AWS started from a one pager that two employees in the Capetown office wrote (forget their names, it's been years) about the potential to sell compute as a service from the newly revamped Amazon.com website backend and servers.
Once the commercial viability was clear, Amazon.com created Amazon Web Services. The term 'offshoot' is perfectly reasonable.
This is from working at AWS circa 2013, which was just a few years after it started.
AWS: Bezos API memo -> internal infra services that were external ready -> polishing and exposing those one-by-one
GCP: Internal architectural/technical excellence -> new org that attempted to productize v2.0 of those services
Azure: Believe it was mostly ground-up build as a new org/product?
(No idea where Oracle cloud came from, internally)