HT Games
No—they are separate services. Xbox 360 uses Xbox Live (legacy), while Xbox One/Series X|S use Xbox Network.
| Feature | Xbox 360 (Xbox Live) | Xbox One / Series X|S (Xbox Network) |
|---|---|---|
| Online Multiplayer | Requires Xbox Live Gold (legacy) | Requires Game Pass Core / Ultimate |
| Party Chat | 360-only parties | Cross-gen (One/Series/PC/Mobile) |
| Cloud Saves | Separate 360 cloud | Unified Xbox Network cloud |
| Marketplace | Xbox 360 Store (limited) | Microsoft Store (unified) |
| Gamertag / Achievements | Shared (syncs) | Shared (syncs) |
| Backward Compat | N/A | Plays select 360/OG Xbox games |
If you play on both, you need both subscriptions (or Ultimate which covers One/Series/PC only).