What's the difference between "noun to verb" and "noun that verb" in meaning?

Is there a subtle difference between those sentences in meaning?

1. A hero is a brave person who does things to help others.
   


2. A hero is a brave person who does things that help others.

Answer

Yes, there is a very subtle difference in meaning. In the first sentence, the emphasis is on helping others:

A hero is a brave person who does things to help others.

In the second sentence, the emphasis is on the actions (things) that are done by the hero:

A hero is a brave person who does things that help others.

You'd more likely use the first example for a hero who seeks out people who are in trouble and then does things to help them - imagine a hero who rescues people from captivity. The emphasis is on the people.

The second example would be for a hero who does things that are good, with the goal that some possibly unknown people might benefit from those actions - imagine a hero who kills an evil witch. The emphasis is on the heroic action.