Here's a kind of a generic timeline.

One of the main things to remember is that JMP, JCM 800, JCM 900, etc don't really mean too much, other than define the era they came from. JTM's were the earliest amps, and were a bit different, kind of an experimental time, with two transformers, tube rectifiers etc. Then the JMP, JCM 800, JCM 900, JCM 2000. All had different models in the "Eras" and the model number is what you need to pay attention to.
Late 60s early 70's Marshalls main amp was the 1959 Super Lead. In '76, Marshall modded it, and add a master volume, and a gain stage. Not a tube, but utilized an unused gain stage in one of the tubes and called it the 2203. They were the JMP 1959 (100 watt) and 1987 (50 watt) non master heads, and 2203 (100 watt) and 2204 (50 watt) master volume heads..
In '82, their contract ended with the Rose company, who was a financer, and it wasn't a good relationship for the most part, and in order to break away and start a new era they cosmetically changed things over to the "JCM 800" series.
They didn't change the models or numbers, so they're still the 1959/1987 and 2203/2204 heads. They also had combo amps, and other amps, which all had different model numbers. As well as the 2210/2205 Channel switching JCM 800's. The 900's had their numbers as well, the 2100, 2500, (SL-X and Mark III) 4100, 4500 (.Dual Reverbs) as well as the combos. The JCM 2000's had the DSL 100 and TSL 100 etc.
So, yes, the JCM 800 2203 is the "Same" as the JMP 2203 circuit wise, although different components along the way, changed the way they sounded to some degree over the years.