Since you're in the US, I will only talk about US-spec CRXes.
There are two generations of CRX. The first generation was available from 1983 through 1987. The second-generation was available from 1988 through 1991. The two generations have different body styles, different engines, suspensions, and are pretty much two completely different cars built with the same mission. (To get two people around economically and enjoyably.)
There are three different trims of CRX within each generation. There is the base (often called "DX" after some later Honda naming conventions, even though there is no "DX" badge on any CRX), the HF (high fuel efficiency) and the Si (sports injected). The HF and Si cars started life with badges on the right-rear of the car that say what the car is, though those are easy to remove or replace.
The original CRXes were all carbureted, and at first were all base models. For the 1985 model year, Honda introduced a new "Si" version with a more powerful fuel injected motor, a sunroof, shorter gearing, and other "sporty" touches. Somewhere around the same point they also introduced the HF version, which was still carbureted but was built more for fuel economy than the base model. All three of these carried on until the end of the 1st-generation CRX with the 1987 model year. I think that by the end they all had 1.5 liter motors, while the earliest CRXes only had 1.3s, but I am not sure on that. An automatic transmission was only available on the DX model, all others had five-speed manual transmissions.
You can look over on Portal - Red Pepper Racing
; those people are fanatics about the 1st-gen CRX, and the Civic generation that it was based on. They know a whole lot more than I do.
In 1988, Honda introduced a completely redesigned CRX based on the newest Civic platform. It continued the same three trim levels that were available fir 1987; base (DX), HF, and Si. The Si had a new 1.6 liter motor; the DX was changed over to Dual-Point Fuel Injection (DPFI, a type of throttle-body injection) on its 16-valve 1.5 liter motor, and the HF was changed over to Multi-Point Fuel Injection (MPFI), similar to what the Si had already, but on an 8-valve 1.5 liter motor.
All of the Si cars came with a power-operated sunroof; none of the others had one from the factory. The Si also had the rear window wiper and left and right exterior mirrors. The latter two were options on the DX and HF models. Again, the HF and Si were badged as such, while the base model was not. The Si had fairly short gearing (3000 RPM at 60 MPH) for more sporty performance, while the HF gearing was taller for better fuel economy. The DX was available with an optional automatic transmission, neither of the other two were.
In the US, 1989 saw the seat-belt attachments move from the chassis of the car (the B-pillar) to the door in order to meet new "passive restraint" laws. This happened on the DX and Si models, but not the HF. In 1990, the HF belts were also moved to the door.
The cars got heavier over the years, as most do. The early cars were the lightest, the last cars were the heaviest. The HF cars were lighter than the other trim levels, while the Si cars were the heaviest trim level.
Engine swaps, particularly for the 2nd-gen CRX, are fairly easy and not uncommon. So are badge swaps. You can tell what trim level the car originally was by checking its VIN number (there are decoders out there), but it is usually best to check for the engine code (on a boss on the front part of the engine block near the transmission) to tell what is really in there. Transmissions are less easy to determine, so it may be easiest to see what RPMs the engine turns in 5th rather than look for transmission identifying marks.
The folks over at CRX Community Forum • Index page
know an awful lot about 2nd-gen CRXes (and somewhat less about 1st-gens), and are a lot easier to read than honda-tech is.