@parautenbach is correct. You are confusing terminology.
REMOTE means you can connect to your Home Assistant server from another network. For example, in a restaurant on their WiFi you want to check if you turned off the garage light.
LOCAL means everything on your home network whether it’s connected by WiFi or Ethernet. It’s the first letter in the acronym LAN.
The only way to get remote access is to expose your Home Assistant server to the Internet. Some people use port forwarding through their Firewall and DuckDNS for DNS resolution. Others subscribe to Nabu Casa which, I believe, tunnels into your server like a VPN. I’ve done both and much prefer the Nabu Casa route. It’s much easier to set up and the monthly subscription supports Home Assistant development.