What kind of graph is used to compare data that does not change continuously?

If the data does not change continuously, it is called discrete data, and is commonly compared by use of a bar chart.

Technical note: please note the use of the Word chart, graph is commonly misused in a mathematical sense like this. A graph, mathematically, is a series/group of nodes that represent information and are connected by lines/edges that represent a link to other information. Bar graphs, line graphs, histogram graphs, bubble graphs, area graphs etc, are all technically chartsnot graphs. For more info see the link below on graph theory.