The terms are misused on a regular bases.
Unfortunately there are no Urethane police.
Your ex-company is one of the very worst for playing games with the name.
In short a true polyurethane resin will have good flexibility and NEVER need a flex agent.
In short if you look at Acrylic urethane under a microscope you see the resin structure looks like a ladder (in short terms)
A polyurethane will look like an over reinforced (many times) house Gable.
Activation of Polyurethane will be 3:1, 2:1 or 1:1 as it takes more isocyanate's to lock the product down where an acrylic urethane can be activated all day long with a 4:1 mix.
Polyurethanes usually end up with a 2 pencil hardness witch is softer than an acrylic urethane, so this gives it much more stone chip resistance and a lot better adhesion.
Polyurethanes will be much more resistance to harsh chemicals and that is why on jets its a requirement.
Up until 8-9 years ago Polyurethanes were very hard to buff and to lay with out orange peel was almost impossible except where you ran it.
This has all changed as there is no longer a spraying difference
between the resin systems, if the company is using newer resins.
A well made Polyurethane will also have more clarity(cleaner gloss) than an acrylic and most true with excess coats such as
Another benefit is is easier to make a polyurethane to buff good even 30-60 days later where a lot of clears after 3-5 days forget it on the buffing. Not all polyurethanes are easy to buff 30 days after painting but it can be done if the company wants to put the effort into it. This is very important for restoration as were painting the car in pieces off the frame and it may be 60 days before the car is put together and can be wet-sanded and buffed.