One of the jobs of a router is to connect networks that have physically different transmission media. Twisted-pair Ethernet is extremely common these days, but fiber (Ethernet, SONET/OC, and others) is used for most high-speed or long-distance runs, and different types of layer-2 and layer-1 networks have been used in the past and are still in use today, such as T1/T3 lines, ISDN, and Token Ring.
For historical reasons, serial cables such as HSSI may be used to connect equipment such as T1/T3 terminating devices. These will show up as
interface SerialN, and you can get detailed information on the hardware installed in a router with
show controllers serial.
Unfortunately, "DCE/DTE" technically applies to a number of different hardware signaling schemes. In the context of networking, it's most likely to refer to a serial interface that's used to connect to a WAN drop.
In the case of your simulator, you should practice with both types of interfaces. In most business networks, the "inside" interfaces will be Ethernet, while the WAN interface will be either serial or Ethernet depending on what service the telco is providing, and you'll need to be able to configure either one.