Theme Twentyfifteen only has the template for displaying link post formats. It is used for both single and index/archive/search. The styling in its CSS pertains to all of the formats:
Theme authors define what formats they support, and they should style those formats appropriately. Before version 3.1, categories were used in arbitrary ways to show different formats.
Some standardization by theme authors is expected. For instance, Asides should not display a title. Galleries should display a photo on the left hand side with the title shortened and to the right. Long format posts should have a double line underneath them.
If your theme takes advantage of these Post Formats, you will have any easy way to display each format with a unique style.