home.php is a reserved file name on some servers and may be loaded in preference to index.php. front-page.php sounds like a generic custom page template.
Personally I’d suggest avoiding home.php as a template filename. It may cause problems at some point.
No, it’s not a generic custom page template. front-page.php is a new Template File in WordPress 3.0+.
I am sure that the wordpress developers think something with these two template files. But what? Thats the question.
home.php is applied on the main blog-post listing. If you use Settings -> Reading to change where blog posts are displayed by default, this template file is different then front-page.php.
front-page.php could also display the latest posts on your homepage, but if you’ve altered the settings so that a Static Page is your homepage then this file would be used to display that (assuming you haven’t given that page a specific page template file to use).
There is a good bit of information about Template Hierarchy here — http://codex.ww.wp.xz.cn/Template_Hierarchy
