"Bedrock" refers to the Minecraft editions capable of crossplay. The game is indeed the continuation of MC:PE, but simply now available on Windows 10, Xbox One, Nintendo Switch and more. "Vanilla" refers to any version of Minecraft with no mods (or resource packs/data packs/plugins, depending on context). Someone can say "Vanilla Bedrock" or "Vanilla Java", depending on the situation. Java of course refers to the OG, Java version of the game, available on Windows, mac-OS, and Linux.
Hopefully that clears things up for you.