Hello there, s_betty.
You are correct in your understanding that Home Sharing requires the devices needing to be signed into the same network. The following Knowledge Base article offers up some great information:
Troubleshooting Home Sharing - Apple Support
Although the entire article is very useful, the section that is relevant to your question is the following:
Home Sharing requires a home network with an active Internet connection. All the devices you want to use with Home Sharing need to be connected to your home network.
In addition, verify that:
- All your devices are connected to the same router, if you have multiple routers. Using multiple routers may prevent discovery between these devices.
- Your devices are not using a Virtual Private Network (VPN), or that they are all on the same VPN. A VPN may isolate the device and cause connectivity disruptions.
- If you have a router set up with a guest network, make sure all devices are either connected to the guest network and devices on the guest network are allowed to communicate with each other, or switch all devices to the primary network on your router.
- If your computer is asleep or shutdown, or iTunes is closed, there's no access to the shared iTunes library. Wake up or start the computer and open iTunes to regain access to that library.
- Your router needs to be up-to-date. If you are using an AirPort or Time Capsule, learn about firmware updates. If you are using a router from another manufacturer, contact the manufacturer to inquire about available updates.
Thanks for reaching out to Apple Support Communities.
Cheers,
Pedro.