Upgrading My Tower

My set up includes a desktop tower running as a file server. I am considering a rack server that would give me room to expand and plan for future, because currently I am restricted to whatever my tower can hold. Though, my knowledge of servers and their internal workings are little to none. So, I was wondering what would be better a blade or rack server? Is there any advantages to using one over the other?

On the topic of my ignorance, I am very extremely familiar with hardware on a desktop level, but I don't know where to start with server hardware. Could someone explain the basics?

Thanks for reads!

Well, you can pack more blade servers into a space than you can 1U rack servers, though both are usually rack mounted. The racks themselves are bigger than a tower, or even a couple of towers, generally, so if you're looking for space savings you might not get it unless you're going to be adding a number of servers.
Blades are generally more expensive than racks for a small number of servers.

Either way, multiple servers is quite a lot for a home file server (though undeniably high in geek desirability factor), what exactly is it that you are outgrowing in the current box?