Below I'll use "Lexus" to mean those cars that get branded that way when marketed is the West and "Toyota" to mean to the ones that get branded "Toyota" in the West. I'll use "the company" when referring to Toyota the company rather than non-Lexus cars the company makes.

I'm curious if there is any difference within the company other than branding.

Are they built at the same factories, or are there separate factories for Lexus?

Are there separate engineering and/or design organizations for Lexus and Toyota that independently hire engineers and/or designers, or are engineers and/or designers hired by the company and work on whatever mix of Lexus and Toyota projects that the company wants to assign them to?