I would like buy a cellar for aging wine at home, but I don't know if the white and red wine can be kept in the same cellar.
Maybe at the same temperature?
There are cellars refrigerated with two zones but this is not for preserving wine.
All wine that you want to age for a long time should be kept at the same temperature. The difference in temperatures come when you want to serve the wine. White should be served at a lower temperature than cellar temperature. Red wine, ideally, should be served at cellar temperature. What is the ideal cellar temperature? That is open to debate, but somewhere in the low 50s Fahrenheit (about 11-12 C). Humidity should be kept constant around 75% but there is no evidence you need to keep the humidity that high. You do not want to keep it at an excessively low humidity. You are trying to make sure the corks don't dry out which can cause wine leaking around the cork. You also want as little light and vibration as possible. Think of a cave as your ideal storage facility. You can read the Wikipedia article about Wine Storage