The term “transit” most often refers to IP transit, where you’re paying a third party to reach all other networks besides your own. This is usually what we call Ip and operates at Layer 3 of the OSI model. This is the “IP” in TCP/IP.
The term “transport” is more loaded – it refers to physical layer technologies. Things such as Ethernet, leased lines, waves, and other technologies to “transport” the IP from one place to another. Think of transport as the water pipe and transit as the water.