I use VillagerNames (by you) and VillageNames (by AstroLibs)
https://www.curseforge.com/minecraft/mc-mods/village-names
Minecraft version: 1.12.2
Forge version: 14.23.5.2855
Environment: Singleplayer and Multiplayer

Mod name: VillagerNames
Mod version: 2.9

My main qustion is: does the two mods the same? If not, are they incompatible?

They should work together without problems. Villager Names sets the name tag of unnamed villagers, so it doesn't interact in a special way.