To clear up possible misunderstanding… 802.1q and VLANs can be used with L3 routed connections (see below). The way to understand this is when a frame arrives on a subinterface, the physical interface receives the frame and reads the 802.1q tag to determine which subinterface to direct the frame for processing. Return traffic gets encapsulated in an L2 frame with an 802.1q tag (in the example below the tag = 100). If the frame doesn’t have a tag, then it’s processed by the main physical interface.
interface gi 0/0/0
no ip address
!
interface go 0/0/0.100
encapsulation dot1q 100
ip address 10.1.100.1 255.255.255.0
A layer 2 connection, like a VPLS (ENS for Comcast or ACE for AT&T) is basically the ISP offering you a virtual switch to plug into between your sites (or the cloud) meaning all devices that have circuits terminating on that virtual switch (the VPLS) can talk to each other over layer 2. For instance, your devices may see each other through CDP. Some ISPs charge extra to pass CDP, but the principle is the same.
Of course a circuit doesn’t need to be a VPLS to offer L2 connectivity, that’s just one example. A circuit could be a point-to-point and also offer L2 reachability. That said, you’re not going to get traffic beyond a L3 hop (like a router) without an IP address.
A L3 circuit usually means you’re peering at L3 with the ISP. Your router connects usually via a dynamic routing protocol (BGP, EIGRP, etc…) to the ISP router. They take whatever advertised routes/prefixes you advertise and pass it to the other end of the circuit, where there’s another ISP router that peers with your far end router, again over L3 and passes the traffic.
The advantage of an L2 circuit is that you don’t need to interact with the ISP to connect your A-side and Z-side devices. The ISP turns up the circuit, you accept it, then you configure each end(s) and you’re done. The other advantage is that you don’t consume additional IP space peering with an ISP, though ISPs can offer public IPs to peer with even though the connection remains private.