No, a single speed is a bike with one gear and a fused gear has none, but that only effects the rear wheel which you fortunately still have (you can tell the bike is SS or fixed as there is no rear dérailleur for changing gears because there aren't any to change). But you must know that as its your bike surely?!
The wheel size is 700c, the rim width is the 622 I believe and the tyre width is 23mm, you'll need to buy one of those too, and an inner tube
A vittoria rubino tyre is reliable and costs a tenner from wiggle in the 700x23mm size you need (you'll need an inner tube that is 700x18/25, probably with a presta valve)