A thermal chimney is a passive technique to encourage air movement and ventilation in houses, especially those in regions with less natural air movement.

It works on the basic principal that hot air rises. This air is lighter and expanded in comparison to the colder air at the bottom of a space.

The biggest component of a thermal chimney missing from most homes is the outlet for the air at the top. Less frequently missing is the inlet at the bottom of the house. Once you have operable openings at the top and bottom of the house, you have the makings for a ventilation system that has the potential to greatly reduce the cooling loads on the house by drawing the warm air up and out of the home.

There are variations including direct solar assistance which would increase the temperature of the hot air at the top of the house. This would aid in creating faster currents, pulling in more colder air at the bottom of the house.

Sounds like cross ventilation with a vertical component. Is that all this is? How are they different?

Cross ventilation takes advantage of air movement through the home by allowing the wind to blow through the home taking warmer air with it. Its not really the same. Stack ventilation or thermal chimneys work with different principals, but both can help with creating more comfortable indoor thermal environments.