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F-16Cs are Block 25, 30 and 32. F-16CGs are Block 40/42s. F-16CJs are Block 50/52s. Recently, the use of the unofficial term CM designates a Block 40/42 or 50/52 with CCIP mod which essentially levels the field between them and renders the CG/CJ designations obsolete. You will occasionally see F-16C+ in various places, which is fairly convoluted, and has to do with various upgrades to the series such as CUPID but the essential math on that is a C+ is a jet that is able to use targeting pods and GPS guided weapons.
Block designations: F-16s were built with Pratt & Whitney engines from day 1. The C models used the F-100-PW-220 in the first production Block, the Block 25. Up until that point, F-16A/B Block #s had been 1, 5, 10, 15 and 20. The 25 was a continuation of that Block designator system. The Block 30 was slated to merely be the same progression, but it was decided that General Electric produced a great fighter engine, the F-110-GE-100, and since Pratt had the F-15C/E contract locked, it was unfair that GE was frozen out of the F-16 production. The original intent was to have the engines be interchangeable between airframes. The Block designations were changed to reflect which motor was installed in the Block 30 series. A Block with 0 is a GE so the Block 30s are GE powered. A 2 designates a Pratt powered jet, so the Block 32s are Pratts. The Blocks are the same otherwise……same jet, different engines.