It will depend on the sample size. If the sample is large the two will be very close. You will see at the bottom of many t-tables a row for df = infinity and then it follows the normal (z) distribution.

Sergio

Try this:

Z-score = T-score - Reference T-score

T-score = Z-score + Reference T-score

Try this

http://www.differencebetween.net/miscellaneous/difference-between-z-test-and-t-test/

Thank you very much for your answers, they were useful.