Cross-Play: Xbox Minecraft vs PC Minecraft? Only If Both Are Bedrock Edition

No — they are separate editions with no cross-play.

Editions

• Minecraft: Bedrock Edition — Xbox One/Series, PS4/5, Switch, Mobile, Windows 10/11 (Microsoft Store), Fire TV. Cross-play enabled.
• Minecraft: Java Edition — PC/Mac/Linux (launcher). No cross-play with Bedrock.
• Xbox 360 Edition / PS3 Edition / PS Vita Edition / Wii U Edition / New 3DS Edition — Legacy, discontinued, no updates, no cross-play.

Your Scenario

• "Xbox Minecraft" = likely Xbox 360 Edition (legacy) or Bedrock on Xbox One/Series.
• "Computer Minecraft" = likely Java Edition (Steam/launcher) or Bedrock (Windows Store).

When Cross-Play Works

• Bedrock (Xbox One/Series) + Bedrock (Windows 10/11, Mobile, Switch, PS4/5) = YES.
• Java (PC) + Java (PC/Mac/Linux) = YES (via LAN or server IP).
• Java + Bedrock = NO (officially). GeyserMC proxy enables it on custom servers (technical).
• Xbox 360 Edition + anything = NO.

Check "Edition" on title screen. Buy Bedrock on Windows Store to play with Xbox console friends.