FrostWire is a free, open-source Gnutella client and a fork of the LimeWire source code (and as such, it functions exactly the same). When you search for a file using FrostWire, you get results from LimeWire and vice versa.
However, the user experience differs in two ways. One is that the code is actually based on LimeWire Pro, the paid version of the popular P2P client, so users don't have to worry about simultaneous download restrictions, and they won't get bombarded by ads. Also, befitting the name, the interface has changed from green to blue and has been slightly improved. Tabs have rounded corners, and there are two additions, as well. Connections monitors your outgoing and incoming connections by host name, but also provides bandwidth information, the vendor and version being used, and more.
While some people have experienced faster download times with FrostWire compared with its parent, others have not. FrostWire and LimeWire are practically indistinguishable, although the lack of ads is a big plus.