CONSERVE meaning is to use things wisely because it may be impossible to replace them. That's why it is always advisable to conserve(use wisely or don't waste) natural resources like water or crude oil, so that future generations may also get benefited from them. PRESERVE simply implies that you are trying to attempt to keep something as it is. For example, we put our efforts to preserve historical monuments. Please ignore any grammatical mistakes, I am an English learner.

To any American or native English speaking person the distinction between conserve and preserve would be very much like splitting a hair. They're basically one and the same.