A file with an .ai extension is an Adobe Illustrator Artwork file that contains vector graphics on a single page. It uses points to create paths for displaying the image data, thus making it safe from losing image quality if it is enlarged. AI format finds its major usage for logos and print media. AI files can be opened with Adobe Illustrator, Adobe Acrobat DC, PaintShop Pro, and CorelDraw Graphics tools.
An XPS file represents page layout files that are based on XML Paper Specifications created by Microsoft. This format was developed by Microsoft as replacement of EMF file format and is similar to PDF file format, but uses XML in layout, appearance, and printing information of a document. It is, in fact, more justified to say that XPS is an attempt on PDF, but couldn't get enough popularity as owned by PDF for a number of reasons.
You can also convert AI into many other file formats. Please see the complete list below.