A prop house is a trading room solely trading its own money, this is a house that backs the traders and pays a percentage of the profit but accepts all the associated risks. Typical examples Atlas & Trading Connections.
An arcade (or as we prefer to call them trading room) is a place where market connectivity and facilitation is provided but the clients are self financing. As a result the company providing this facility is generally a member of the exchanges it clears and is FSA registered to hold clients funds. Typical examples Fortis & Kyte.
Another slant is a trading room which offers connectivity, is a member on all the exchanges and FSA registered but Introduces the clients to a Bank or clearing company for clearing. Example Xconnect.