Oh dear Lets clear it up a bit.

T34 comes from the fact that the rear housing is a T3 flanged one, and the front housing is a small T4 one, ie its a T3/4 (an RS500 is a T3/4 actually too, jus a bigger one).

T35 and T38 are TBH more real terms as basically that just gives an estimation on size, ie more than a T3, but not a T4.

Same as T2s, T25s, and T28s, its the way they name general turbo sizes.

There are still hundreds of variations of each of the above though.

So to sum up, an EscCos turbo is a T35, which is a T3/4 turbo.