I'm sorry for the delay but I'd turned off my computer
for the evening before you posted your follow up.
Every state has a disorderly conduct statute, which is a catch-all criminal statute and some form of a harassment statute. The elements of the crimes and the level of the offense and the penalties may differ from state to state.
However, your convictions were New York convictions, and are violations.
If you want to compare the statutes, however, here's NY's disorderly conduct statute followed by Texas's:
And here is the New York harassment statute followed by Texas's: