Also I don't really understand what the difference between the tiagra and Ultegra brake levers are except in comparison to like bottom rung stuff. But to each other I can't seem to tell a difference.
But you're making an invalid comparison: the real comparison is between Ultegra and 105. The two are functionally the same, but Ultegras are a bit lighter and use better materials (probably carbon fiber handles, for instance). The year I got mine, the 105s were physically larger too, so the internals weren't as advanced; not sure about today.
Tiagra is a 10-speed shifter, while Ultegra is an 11-speed, so they're certainly not compatible at all. You can assume that Tiagra will be even more cheaply-made than the 105.
But you're making an invalid comparison: the real comparison is between Ultegra and 105. The two are functionally the same, but Ultegras are a bit lighter and use better materials (probably carbon fiber handles, for instance). The year I got mine, the 105s were physically larger too, so the internals weren't as advanced; not sure about today.
Tiagra is a 10-speed shifter, while Ultegra is an 11-speed, so they're certainly not compatible at all. You can assume that Tiagra will be even more cheaply-made than the 105.