I'll give this a go:
The transmitter (TX) and Receiver (RX) are independent systems. I'm not sure why, but I image it has something to do with one breaking, the other one remains functional. Depending on the airport layout or type of air traffic facility(TRACON/Center), TX & RX are located at various locations around the airspace. For example, Oakland Center is in the East Bay of the Bay Area,CA but they have communication sites out in Fallon, NV since their airspace extends that far East.
Your second picture must be newer equipment. Maybe at large, re-modeled, new, or test facilities. The first picture is called an ETVS or Enhanced Terminal Voice Switch. It's the most common and a combination telephone and radio communications system.
As others have said, a Tower is responsible for movements on the ground, runways, and usually a 4 or 5NM ring up to about 5,000' around the airport. You can use VFR sectional to determine a Tower's airspace.
TRACONs are responsible for usually an area of about 20-50NM around a primary large airport up to around 18,000'. Again, the dimensions vary though depending on the complexity of the airspace. For example NORCAL handles airspace around SMF, OAK, SFO, SJC, etc.
Centers usually handle hundred of sq. miles of airspace up to 50,000' (if I recall correctly)...maybe it's 80,000'. You can find Center boundaries fairly easy via google.
So naturally, Towers are located at airports. Some Towers incorporate TRACONs. So Controllers work both up in the Tower and down in the TRACON. Some Towers and TRACONs share a physical building/location but Controllers only work in the TRACON and others up in the Tower.
Some TRACONs & Centers work the same way where a Center incorporates a TRACON and the Controllers work both, one, or the other. Again, they may share the same building/location.
And in other cases, Towers are at the airport, TRACONs are miles away in other cities, and the Center is miles away in a third city. For example, RNO Tower is located at RNO airport. NORCAL TRACON is in the Sacramento area, and Oakland Center is in the East Bay Area.
As for the take-off/landing radio procedures. Head out to your local airport with a scanner, binos, and a comfy chair and watch and listen.