what are the differences between the transport proteins and the carrier proteins in the cell?

Answer 1

Transport is a more general term.
Transport proteins can be carriers or channels.
Carriers bind the small molecule that is going to be transported and flip from one side of the membrane to the other. or change their shape so that the molecule binds while being on one side of the membrane and is released on the other.
Channel proteins, as the name indicates, create tunnels in the membrane through which molecules can pass. The size of the opening and some additionals things make the channels specific to certain molecules. Also the channels can open and close according to the cell's needs.

Answer 2

Transprot Proteins are the one transporting molecules. While Carrier proteins are proteins in the membrane a cell, they carry proteins inside the cell, this is called facilitated diffusion.