I'll try to explain in a simple way:
Spytech:
Applicable for both teams. Incorporates surrounding environment in some way (2fort's basement rock exposed, sawmill's rainy basement, etc.) I'd look into Googie maybe, it's a very modern style that fits spytech pretty well. A lot of the Spytech areas in TF2 are based off of old
70s IBM and other military data centers. Spytech in TF2 is very clean typically, not much laying around on the floor in terms of junk. Computer models, maps, war rooms, meeting rooms, just try to make it look very active and in progress. Have computer noises, computers flashing, etc. They have white tile or team colored floors, concrete and team painted walls.
Red's architecture (typically):
Pre-industrial revolution, A lot of wood, warm colors. Most of the lights are single light bulbs that cast warm lighting, lanterns, small spotlights, or naturally lighting. Many of their building's bases are agriculture based or just older practices in general. 2fort is a good reference map for the massive divisions between Red and Blue's theme. A lot of curves and angles with variations in height. In terms of materials, brick, wood, rarely any metal. If so, it's probably rusted or some kind of iron. Iron is preferred against blue's Steel, mostly because iron is an older practice that came before steel, steel also has a much more industrial tone to it. (see foundry)
Blue's architecture (typically):
Post-industrial revolution, a lot of metal and concrete. Cool colors are used on blue's side. You see many florescent tubing, flood lights, spot lights, etc. Most buildings are square, cold, blocky, with a lot of concrete blocks. It's a bit more cleaned up than red's bases. As opposed to hay, wood planks, and buckets, you'd see welding machines, steel beams, and oil drums. Again, square and cold is the goal typically. In terms of architecture, look up brutalism or just steel factories in general. Blue is more corporate and less personal, they specialize in metals, large scale industries, sciences, and mining. It's rare to see a full blue-sided buildings, but most are in general use the materials of blue concrete block, concrete floors, mostly clean metal walls, grates, and if they have to use wood, typically a white washed or white bleached walls. Their colors are mostly blues, orange, white, grey, and occasionally green.
Let me know if you're curious about other themes or TF2's architecture in general. Think of cheesy 60s bond films. Those are the most vital references.