Short version: if your 1/4-on or 1/2-on leads with your left hand and you twist left (or vice-versa), it's a Kaz. If your entry leads with your left hand and you twist right (or vice-versa), it's a twisting Tsuk.
Long answer:
A left-handed roundoff actually twists to the right. What this means is that when you do a left-handed entry and twist left, you're switching directions. Keep this in the back of your mind through the next part of this.
Now, in a Tsuk, you come off the table, square up towards the table, then perform a backward salto. To do a Tsuk with a 1/1, you square up towards the table and then do a back 1/1.
However, in a Kaz, since you're changing directions, you never square up towards the table; you turn the opposite way, square up facing away from the table, and do a forward salto. Add a 1/2 twist to the front salto, and it ends up looking like (and landing like) a Tsuk 1/1.
The Kaz, imo, is easier, because you only have to do a 3/4 twist after leaving the table, whereas in a Tsuk 1/1 you have to do a 5/4 twist.