Analytical writing comes in many forms. Regarding art, it concentrates on the components of the text as a whole to determine how they work together (successfully or not) to create a certain effect, evoke particular ideas or emotions, etc. This type of writing is also applied to specific characters we meet in life or literature. It may also come in the form of a film, music, book, exhibit, or restaurant review, in response to an article, or as a cultural critique.
Many of the writing modes overlap or work together to create a successful piece of writing. For example, notice how the focus of this research essay is cultural critique, where analysis is a primary method of building evidence to support an argument-based claim: