What are the similarities and differences between savannas and steppes?

There are several types of steppes, and the savannah is one of them. What unites them all is that these are fairly flat areas with a predominantly grassy cover. And they differ in that the savannahs are in warmer and wetter zones, there are rainy seasons, due to which some types of trees can also grow. And the food supply is sufficient for a large number of large animals. Grasses grow in the northern steppes (real steppes), and due to the rather low temperatures and aridity, trees and bushes are almost absent.