What (if anything) are the standards for "generic" part numbers?
A very few components are actually standardized by JEDEC (think of the 7400 logic series, for example). 

Most of the components you mention are simply results of historic multi-sourcing agreements: Large customers (esp. of the military kind) wouldn't buy an obscure part that they could only get from one party.

Also, don't underestimate the history of these companies: for example, TI having all the parts that are still available in stock under the brand name of National Semi happens because the former bought the latter, and some stocks simply have a half-life of roughly eternity. Mergers and spin-offs sometimes leave multiple parties with access to the same IP.

To answer about guarantees: Um, these usually don't exist. Good luck out there and read your datasheets!