They're part of the same family. YJ-81 is domestic and C-801 is export. The change from YJ-81/C-802 to YJ-82/C-802 is from rocket to turbojet, which increased the range. YJ-82 is domestic and C-802 is export, with the export using a French turbojet and the domestic using local turbojet. YJ-83 is improved YJ-82 on electronics. Then over the years, the missile is evolving on the engine and electronics, including the KD-88, which replaces the seeker for a TV unit and used for land attack, sort of like a SLAM and SLAM-ER. The latest ones as per the export market appear to be the CM802AKG, which is air launched and used on ground targets.
This big evolution can be expressed in the range, with the C-801 at 40km with its pure rocket motor, and by the time you reach the CM802AKG, it reached 235km from an air launch. However, back in 2005, a JH-7A fired a YJ-83 over a tracked range of 255km, so the Chinese might be coy on the actual missile ranges. Then you now have this sub launched CM780UN which is pushing the range to 350km.
You can't be shy about the potential brought by electronics improvements, since it allows for things like inclusion of datalink for mid guidance control and retracking, much improved resistance to ECM and decoys and the potential to add evasive maneuvers. Improvements also goes from a single active radar seeker to optical TV guided systems for land targeting, and adding IR imaging which makes the missile very difficult to fool since it compares target images to its built in database.
I believe at some point the PLA Navy interest on the YJ-8X family has dimmed at some point, as they shifted to the YJ-62, YJ-12 and YJ-18, and even possibly a YJ-100 (likely based on YJ-62 and VLS launched), all for the top end. But defense industry still feels there remains potential for export sales, and you still need ASMs to deal with the niche of targeting smaller ships. And then you still have a huge inventory of ships that use the YJ-83, like all the Type 054As, Type 056s, legacy ships, Song subs, Type 022 Houbeis of which there are over 80. Another is that the PLAAF seems to take over interest on the family for use as an air to ground weapon.