Say you want to connect an office in New York with an office in California. To do so, you could contact a frame-relay, x25, ATM, or MPLS provider. These providers have meshed together many regions, states, and countries so that your communication can travel across their backboned network. This eliminates the need to run a cable directly from office to office. It is scalable, because you can add another office to the provider's backboned network very easily.
Leased lines, according to the CCENT/CCNA, is usally a direct line from one router, or network, to another. This would generally be PPP or HDLC.
I am not entirely sure about TDM and STDM. Usually, only software engineers/developers are concerned with these features.
ATM, X25, Frame-relay, MPLS communicate over their own backbones; they are their own layer 1 & 2 protocol, more or less. Google: "MPLS backbone", "ATM backbone", "Frame-relay backbone", "x.25 backbone", and look under images.
These connections are generally serparate from the Internet, and therefore they do not use DSL, cable, etc.
