When someone’s purpose is to describe a problem and evaluate possible solutions, he/she will write a problem solving essay. In academic writing, the problem solving essay is very common and useful. For example, students would use it in a ecological class if they were asked to discuss solutions to the problem of endangered species.
Comparison is an act of examining resemblances. That means when someone compare two things, he/she look for how they are similar. Contrast is an act of distinguishing by comparing differences. That means when someone contrast two things, he/she look for how they are different.