When saving a List or Document Library as a template, what is the benefit of having a different filename and template name?
You will see the benefit when you upload the template file back to a site collection.
To upload the template, you goto Site Settings -> List templates. You will see the list template gallery which works just like any other Document library. You can upload your template file here.
If the gallery already contains the template with filename same as the one you upload, the new one may override the old one. If you choose do not override then you cannot upload the new file. You have to rename filename first.
After you upload the template, the default Template Name is the name you input when you "save it as template" before.
I would say the the filename is just simply a filename as the list template is not stored with the OOTB list templates, you can name it anything you want. But as always, a relevant filename will help anyone in the future figuring out why the template exists and what it is used for.
The template name is the one important, as this is the name that any users adding a new list see's and should be relevant to what the main usage for the list-template is to avoid any confusion.