I don't get it.....bike gurus I need input

The only time an athlete is permitted to use a TT bike (basically one that has pursuit bars and aerobars) is for time trials. In this year's TdF, there were only two; stage 2 which was a TTT (team time trial) where teams start together but are separated from the other teams by a certain time interval (3 minutes?) and today's stage which was an ITT (individual time trial) where all athletes are separated by either 2 or 3 minutes depending on their overall position.

For all remaining stages, athletes must be on bike with drops bars.

Shane

Stage 2 was the team time trial not a road race stage. You race against the clock and start at time intervals, but you do it as a team.

In road racing there are generall two types of races; time trials (TT) and mass start events. In a mass start event, drafting is allowed and therefore all athletes must ride bikes with traditional road setups; these days that means that they will have drop bars and some type of intergrated brifter (brake lever and shifter). In ITT events, as drafting is not allowed, athletes can ride a bike with pursuit bars (bull horns), aerobars with shifters and, since they only need to worry about themselves not athletes around them, will adopt as aerodynamic position as possible for most of the ride. In a TTT (team time trial) drafting is allowed but only between teammates so the TT bikes are allowed for these stages as well under the assumption that the team knows each other well enough to draft off each other on a TT bike (this is not always the case; there are often many crashes during a TTT).

Mass start - road bikes, many different teams


TT - TT bike, individual rider


TTT - TT bike, one team


Shane

Yea, he dumbed it down for me.  Thanks for the effort.

Time trial bikes and triathlon bikes are configured differently and subject to different rules.

The one with the stronger rider

TT bikes subject to UCI and USAC rules have dimension and angle limits, rules about fairings and other aero techniques, and probably several other limitations. To my knowledge USAT doesn't impose any kind of similar rules and is fairly wide open with regards to the bike itself. I admittedly don't know all the piddly details but that is my limited understanding.