Usually the format you see in themes are content-{$post_format-term}.php or content-{$pagename}.php, but it is not restricted to this formats. The naming convention can also differ to your liking as long as you keep it out of normal template hierarchy and then use get_template_part to call it correctly.
These are not self standing templates, they cannot operate on their own as normal templates do as seen in the template hierarchy. Their role is to house the the loop. Just like the header, footer and sidebar templates, these template parts are the building block for templates, the files used to display the content on the front end.
The advantages of using these template parts are:
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the reuabilty of the loop amongs different templates and different queries
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keeping styling amongs templates
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DRY principle
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keeping template files organised, short, clean and easy maintainable
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avoid unnecessarily long conditional statements in template files, for example when using post formats
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makes specific customizations easier in child themes….
These a just a short list of advantages. It is all up to you and your structures if you want to use it or not. I personally make good use of these templates parts because of the above
EDIT
As for page-{$pagename}.php templates, these are self standing templates which you use to create pages on. These templates are selectable in the pages backend when creating a new page on your site. This template is an organized collection of the header, footer, sidebar and in some case, the content-*.php template parts with the loop.
Page templates, however does not need to follow the page-*.php naming convention (only since 3.4), it can be called anything you like and will work only if
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the page header is correct
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this custom name does not clash with naming conventions as set out in the template hierarchy
Just on your use case with the about page, this will be a very specific page template, so I would simply just create a page-contact-us.php or contact-us.php template with everything inside that.