Application software is grouped into categories based on the main task it is designed to perform, such as word processing, spreadsheets, database management, presentations, or graphics creation and editing.
Adobe Illustrator is a vector graphics editor built specifically for creating and manipulating illustrations, logos, and drawings. Because its core purpose is producing and editing graphical artwork, it belongs to the category of graphics software.
The other named programs belong to different software categories. Microsoft Word is word processing software used for creating and formatting text documents. Microsoft PowerPoint is presentation software used to build slideshows that combine text, images, and transitions. MS Access is database management software used to store, organise, and query structured records. None of these three has graphic creation and editing as their primary purpose the way Adobe Illustrator does.
When identifying software categories, focus on the primary function the tool was built for, since many packages can display images without being classified as graphics software.