Hello Juan
When talking about CAPWAP tunnels, there is really no distinction concerning routed or switched tunnels. CAPWAP tunnels are created between an AP and its WLC over an underlay network that can traverse routers, switches, multiple subnets etc, just as long as the AP can reach the WLC. The CAPWAP tunnel is specially created to carry the multiple VLANs that correspond to the SSIDs that an AP may be serving.
Rene states in the lesson that “Tunneled traffic can be switched or routed” and this phrase may be the source of your question. The idea here is that the underlay network that carries the CAPWAP tunnel can be either routed or switched. Rene goes on to say that this:
…means the lightweight APs and WLC don’t have to be in the same VLAN. This is useful since APs are typically on the access layer, and the WLC is in a central location (core layer or data center attached to the core).
So it’s not referring to the tunnel as a Layer 2 or Layer 3 entity, but in the way the tunnel is encapsulated and transmitted over the underlying (layer 2 or layer 3) infrastructure. Does that make sense?
I hope this has been helpful!
Laz