What is WireGuard, is it a new protocol? Or a new algorithm for implementing an existing thing? (Or something else)
wireguard is a VPN technology that is now integrated into the Linux kernel, and is available on all major platforms.
It distinguishes itself from other VPNs by not having knobs to twiddle. Should a security issue arise, it will be necessary to replace it with a wireguard2 or such. This also means that it's very hard to get it wrong in config; either it works or it doesn't, and if it doesn't, you haven't got it working yet.
It's very fast and very nice to work with.
Wireguard is pretty much half of what you'd expect from a VPN. It does the low-level part (encryption, packetization, session setup, NAT traversal, etc. -- the “actual VPN”) brilliantly, but everything around key distribution is left to external systems. (Tailscale is a popular choice, but by no means the only one.) E.g., you can't connect to vpn.example.com with user foo and password bar and that's it; there needs to be an Ed25519 public/private keypair set up on both sides, an IP address range (essentially a routing table), and so on.
Of course, if you want to connect two static networks, wg-quick is all you need. But for the typical “remote worker VPN”, it's pretty much a (great) building block.