WireGuard creates a peer-to-peer VPN (Virtual Private Network) between two or more peers (endpoints). Nothing fundamentally defines a peer as a server or client: each peer talks to the other, tunneling/encrypting the data between them. (There may be some ancillary settings - such as at the firewall - that may be required on each side of the connection.) Nonetheless, it can sometimes be helpful to use server/client terminology. For example:
A VPN Server listens for a connection initiated by another host/device/service. A few examples: Your OpenWrt router acts as a server when you install WireGuard to enable remote administration and/or remote access to network services that reside “inside” your local network. Your WireGuard 'server' at home can also provide a measure of security when on public networks or bypass geo-restrictions when traveling since your traffic is encrypted through a tunnel to your server and then appears to be originating from your home). A commercial VPN provider's WireGuard peer would be considered a server as well.
A VPN Client initiates a connection to another peer. Your computer or mobile device acts as a client when it connects back to an endpoint (i.e. WireGuard on your OpenWrt router). Alternatively, if you configure your OpenWrt router to connect to a commercial WireGuard VPN service, then the OpenWrt peer itself may be considered a client.
WireGuard can create a Site-to-Site VPN tunnel between two or more separate networks such that they act as one. Here, either or both sides may initiate a connection, and both sides listen for that data. This lets you administer and/or share network resources between the two networks. A common use case for this scenario is linking two remote office networks together.