The Cruze started life as the Daewoo Premiere Lacetti, designed by Daewoo as an example of "Here's how we think the World Car should be done."
This could be considered the "Generation 0" Cruze.
This vehicle, the Lacetti, was then evaluated by various groups within GM, and designated the base for everyone to use, with engineering input from Opel to give it some grunt to survive outside Korea.
This vehicle, built in Korea, and shipped to EMEA and Samercica, came with a 1.8l petrol engine, from the Astra, or a 2.0l turbo-diesel engine. That was the first of the "new" Cruze models, given that GM had sold a re-badged Suzuki Ignis as the "Cruze" in several markets.
This is the real "Generation 1" Cruze, I have a manual diesel, built in 2009 and sold as the 2010 model in Australia.
Then manufacture (really, more assembly, as most parts were/are sourced from Asia) moved to other GM plants, such as Elizabeth in Australia, where design changes were made, the 1.4l turbo-charged petrol engine added, and the original 2.0l turbo-diesel replaced with a gruntier dual-cam unit.
This is the "Generation 2" Cruze, which, after more design modification, such as replacing the rear disc brakes with drums, and putting in a cheaper and less effective lighting system, stated production in the Lordstown plant in the USA. but only with petrol engines. This is the vehicle the USAians refer to as the "Generation 1" Cruze, although it is more like a "Generation 2 with several steps backwards for no sensible reason." Eventually a diesel that had been modified to conform to to US EPA requirements was added, to the line, for a short, possibly experimental, period.
Then the "Generation 3" Cruze was developed, aimed squarely at the Chinese market (i.e. built in Asia, sold in Asia), and while GM was winding up manufacture in Australia, Mexico was being tooled-up to build this for the American market, quickly switched back to Lordstown for political reasons.
And here in Oz, we will be getting the Generation 3 Cruze built in Korea and sold as an Astra. Apparently only with the 1.4l petrol turbo, and possibly only with a slushbox. Sigh.