flat turf, flat AW, national hunt. How do I differentiate in triggers?

This information is not directly available on the API, so you need to use conditions such as:

Markets name does not contain Hrd
and Markets name does not contain Chs
and Markets name does not contain NHF

These conditions will ensure the trigger only fires with flat races.
IF you want NH races then change the conditions to;

Markets name contains Hrd
or Markets name contains Chs
or Markets name contains NHF

If you only want to bet AW races then just use the Betfair abreviation for the racecourses in the conditions

eg.
Markets name contains Sthl
or Markets name contains Wolv
etc.

You may need to combine the last conditions with the conditions to exclude NH races at courses where there are several codes eg. Southwell and Kempton.

A lot of this filtering can be performed in Market Locator.