No, all T Tauri stars are very young, only a million or so years old (it is a stage in the birth of a star). Thus the Sun was once a T Tauri star but as it is now 4600 million years old, it left that stage of its life a long time ago.
T Tauri stars are pre-main sequence stars. They are not a particular star and can vary in size depending on the propagator star and the amount of matter around it. For the individual star [See...
The Sun is the name of a star. For example: when describing the human race, you can say "you are human", but you can't say "human is you". A star is a "sun" to its planets that are orbiting it. To...