The distinctions between the different truss types used in bridges are clear and easy to define. That is not true for building frames and it seems to me that the reason why not is useful in contrasting bridge structural design with building structural design. I’m limiting the discussion below to steel framing, but it could be expanded to include concrete and hybrids.
There is a taxonomy of steel frames for buildings. There are moment frames, where the lateral-load resistance comes from the rigidity of the beam-to-column connections; and there are braced frames, where the lateral-load resistance comes from diagonal braces between the columns and beams. Moment frames can be subdivided into rigid frames, where the connections approach 100% rigidity; and semi-rigid frames, where there is a known relationship between load and connection deformation. Braced frames can be subdivided into core-braced frames, exterior-braced frames, and so on. The problem is that these categories don’t tell us all that much about any given piece of the building. For example, in a Pratt deck-truss bridge, I know that the the web diagonals are primarily designed for tension from gravity load, the web verticals are primarily designed for compression from gravity load, and the chords are designed for tension (bottom chord) and compression (top) from gravity and both tension and compression from wind load. The truss form sets the criteria. If I know that a building has a distributed-bay braced frame with no secondary bracing…I know nothing abut any individual beam, column, or brace. I don’t know which pieces are designed for which loads.
The Park Row Building, on the left above towering over the old Washington Market, fits the description I just gave. Here’s a diagram of some of the wind bracing, from an 1898 article in the Engineering Record:

That gap in the middle looks funny – you can see it in the photo. It’s a light court with wind braces crossing it. Here’s the first floor framing plan:

The building has a funny first floor plan and things get worse from there. Park Row is on a diagonal to the general orientation of streets downtown. The first bay of beams is not the building proper, but rather the sidewalk vault. (If you look very hard, you can make out the words “sidewalk beams” on the left.) The Park Row facade is just beyond that. The building has a very short facade on Ann Street, the east-west cross street to the south, on the upper right, and a longer facade on Theater Alley, a very narrow north-south street east of Park Row. The semi-circle on the left is the group of original elevator shafts. That light court is on the right side of the plan, above the second floor, in the two bays just to the left of the “178” in the dimension line on the right. So the building has three projecting wings (Theater Alley, Ann Street, and the east part of Park Row) and a large block off to the left (from the elevators to the north part of Park Row).
No simple frame description is going to capture this peculiar shape and what it does to the framing orientation, the need for wind bracing crossing the light court, the way that the bracing has to work around the elevator core, and so on. In bridge design, engineering considerations are foremost, and so the designers’ intentions are usually quite clear. In building structural design, all sorts of icky non-engineering considerations come into play – people want to be able to use elevators, people want windows, people have laid out streets in irrational patterns, people have refused to sell their properties to the developers assembling lots for a site – and so the structure has to work around the architecture. To accurately summarize the structural type of this building is to describe the building structure in detail.