A split-tunnel VPN allows a device to route some traffic through the VPN (typically corporate traffic) while sending other traffic (like general internet browsing) directly over the local internet connection. This reduces the load on the corporate network because not all traffic is routed through the VPN tunnel.
Site-to-site VPNs are for permanent links between locations.
Full-tunnel VPNs route all traffic through the VPN, increasing the bandwidth usage on the corporate network.
GRE (Generic Routing Encapsulation) is a tunneling protocol that doesn't encrypt and doesn't reduce bandwidth usage by itself.
Reference:
CompTIA Network+ N10-009 Official Objectives: 3.3 - Given a scenario, configure and deploy common VPN technologies.