What is the difference between .yaml and .yml extension?
File extensions do not have any bearing or impact on the content of the file. You can hold YAML content in files with any extension: .yml, .yaml or indeed anything else.
The (rather sparse) YAML FAQ recommends that you use .yaml in preference to .yml, but for historic reasons many Windows programmers are still scared of using extensions with more than three characters and so opt to use .yml instead.
So, what really matters is what is inside the file, rather than what its extension is.
As @David Heffeman indicates the recommendation is to use .yaml when possible, and the recommendation has been that way since September 2006.
That some projects use .yml is mostly because of ignorance of the implementers/documenters: they wanted to use YAML because of readability, or some other feature not available in other formats, were not familiar with the recommendation and and just implemented what worked, maybe after looking at some other project/library (without questioning whether what was done is correct).
The best way to approach this is to be rigorous when creating new files (i.e. use .yaml) and be permissive when accepting input (i.e. allow .yml when you encounter it), possible automatically upgrading/correcting these errors when possible.
The other recommendation I have is to document the argument(s) why you have to use .yml, when you think you have to. That way you don't look like an ignoramus, and give others the opportunity to understand your reasoning. Of course "everybody else is doing it" and "On Google .yml has more pages than .yaml" are not arguments, they are just statistics about the popularity of project(s) that have it wrong or right (with regards to the extension of YAML files). You can try to prove that some projects are popular, just because they use a .yml extension instead of the correct .yaml, but I think you will be hard pressed to do so.
Some projects realize (too late) that they use the incorrect extension (e.g. originally docker-compose used .yml, but in later versions started to use .yaml, although they still support .yml). Others still seem ignorant about the correct extension, like AppVeyor early 2019, but allow you to specify the configuration file for a project, including extension. This allows you to get the configuration file out of your face as well as giving it the proper extension: I use .appveyor.yaml instead of appveyor.yml for building the windows wheels of my YAML parser for Python).
On the other hand:
The Yaml (sic!) component of Symfony2 implements a selected subset of features defined in the YAML 1.2 version specification.
So it seems fitting that they also use a subset of the recommended extension.