You can't say what template a project is using - they don't use them after creation! A template is a thing used to create a new item, which then goes its own way, the template has no relationship with the new item after it has been used to create it.
The differences between templates are in the fields, screens, issue types, and workflows. There's not a lot of point in an essay question on how they are all currently different (it wouldn't fit within the character limit, way too long to be useful, and would be out of date in a few weeks or months)
Each template is named and described as something appropriate for a certain type of usage, and intended for you to pick the most appropriate and then mould it to your exact needs after using the template to create your project. Knowing the differences between templates isn't going to help you with choosing which template to use - look to what the template says it is for!
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