Yes. Its an important distinction because they are fundamentally different motives. If the motive is money, various strategies can drive up the cost until the behavior is no longer profitable and the bad actors stop. Religion and ideology are completely different beasts and most strategies that work on profiteers only entrench the others.

Just like how robbing a bank may cause terror to the people in the bank or the neighborhood but it was done for profit not politics.

Wealth is the primary means of expanding ones political influence. It’s a primitive tool like a talking stick to coerce all the other monkeys to do shit for you. Trying to gain money is absolutely political

I think you just defined yelling at someone over money to be terrorism.

You can make a reasonable argument that "nothing is apolitical" but but that's not the definition of political being used when people say what terrorism is.

You are correct; that is the consequence of taking the definition to its ultimate conclusion. Either our definition of terrorism is incomplete or our idea of money is.