Transparent here means the use of the relay is invisible to you. If two devices under the same tailscale/Zerotier network can access each other (e.g. in the same lan), then the relay won’t be used. But if both devices are under separate networks (e.g. one in your home, and the other is your phone while outside your home, and both devices are behind NATs), the relay will be automatically used as a bridge so both devices can communicate with each others.

Connections to relays are encrypted, but Zerotier allows you to setup your own relay server if you worry about privacy. Not sure about tailscale.