Transport technology is really about the art and applied sciences of getting things from place to place. It's about getting people and goods from one location to another. Transport technology can be viewed as the tools and techniques for transforming energy into useful work.

An aircraft is a form of transport technology for moving people and goods long distances as fast and safely as possible.
image: R.Conan-Davies
Engineering transport technology is about the economic and safe transport of goods and services. An aircraft would be an example of aircraft engineering (also called aerospace engineering).
Transport technology can be classified roughly on the medium that it needs to traverse. So for example getting though water would be water transport or marine transport. Going across land would be land transport. Going through the air would be air transport or into space would be space transport.
- Watercraft - from a simple raft to complex engineered craft
- Flying craft - from gliders to jet planes or lighter than air craft.
- Land vehicles - from human power wheels, simply rolling to cars
Transport is also classified on the energy sources that drive or power them. For example 'electric powered'. This is often called the 'mode of transport'. Some modes require special infrastructure, such as roads, ports or rails or cables. Combining all these features is called transport engineering.
Communications technology can be viewed as a kind of transport technology, in the sense of being able to move information from one place to another. When the information is more physical such as printed matter or small parcels it becomes part of postal technology.
A vehicle is generally the device itself that transports things. There is a slight distinction in the sense that some transport technologies require specific infrastructure like rails or cables. This parts are not considered an actual vehicle.
What about bridges? this could certainly be consider as part of transport infrastructure. From pushing a log across a river, to placing stones to knotted structures to fully engineered composite bridges.
Other uses of the word transport
Why not simply transport? why transport technology. transport could refer to essentially any kind of movement of matter or energy. The term is used often in other sciences such as in biochemistry and molecular biology to describe proteins and processes that 'transport things' for example electron transport chains, proton pumps and so on.
even in planetary sciences the term can refer to naturally occurring transport mechanisms for say lava tubes are able to transport lava .
In thermodynamics heat can get transported from one area to another more rapidly depending on the conductivity of the intermediate material. Granted the term usually is simply 'transfer'.