Are you skilled at editing your css files? Quite likely that is the main difference if you are looking for a different appearance. If the main difference is static vs. showing the latest posts then you change it in the settings on your theme.
The "pages" themselves are written in php and replacing homepage.php from Theme A with one from Theme B, won't give you the look of Theme B's home page. Depending on many other variables (mostly css), it may even cause errors on your site.
Thank you for your reply. I have some experience editing CSS, but not a lot. I basically want to change my home page to look more like a magazine, with lots of thumbnail photos linking to content on the inside. How hard is this to do with CSS and php?
Sounds more like the html content on the page. The same as writing a post or a page, you could make a page look the way you want in html (or in the WP Visual Editor) and then set that page to be your home page in the WP Settings.
It really depends upon a) what you want to change b) if your changes can be done within the existing theme's framework b) if not, then does the theme have a template built specifically for the home page or not c) if not, can you build one yourself
There are too many unknowns to say. Paste into what?
Themes are built with templates and while there is a general standard for developing a theme, it's not a hard and fast rule. Each theme author may create whatever templates they want as long as they function with the WordPress core engine. So the answer to your question depends upon the specifics of your situation and only you know - or can learn - that.