There are four t's in Hindi and other Devanagri languages.
1. T- as in tea (tip of the tongue to back of the teeth. This is the plain English "T" as in "team".)
2. Th - The same as above, pronounced with an explosion - produced with the tip of the tongue to the teeth ridge but letting out a lot of trapped air - I cannot think of an English analogy for this sound. Just pronounce "tea" letting out all your anger on the T sound. Yes, I know - I didn't get the phonetics prize.
3. Th - place mid tongue to the back of the teeth. I cannot think of an analogy for this, but it is the th in think but without an aspirative/explosive sound.
4. Th - place mid tongue on the teeth ridge and produce an explosive sound: as in "Think" or "thought".

The "h" does indicate aspiration but not excluisively. In in Devanagri there are diferent kinds of aspiration, depending upon which part of the tongue you place on which part of the palate. In Indian names, "th" is used for all, but the first T sound. Also "t" is not used exclusively for the 1st category. For rxample in the name "Vasant" the "t" is of the third category.

In Vishruth, the "Th" sound is of the third category (so maybe the Ruth analogy was wrong. Sorry, I am finding out that I am not too good at this.)

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I searched for aspiration+phonetics and came across this site: http://www.absoluteastronomy.com/encyclopedia/a/as/aspiration_(phonetics).htm