As with the breadboard, your first stop should perhaps be: wikipedia: stripboard
Basically, once you’ve got your circuit completed on a breadboard and want to give it a more permanent installation – but don’t want to design your own PCB – you’d move the components over to one of these (possibly cutting it down to the size you need) and solder them down, recreating the circuit by creating solder bridges (basically enough solder between 2 pads that they end up being connected), wires, and – where needed – cutting traces.
There are a great number of these types protoboards (stripboard as wikipedia prefers), and they each have theirs pros and cons. This one, for example, has a ‘plane’ on one side that you could solder a component to for a commonly used connection like the ground (just like you may design a PCB yourself with a ground plane). The down side here is that the planes goes everywhere and you may easily create solder bridges you don’t want. It’s also smaller than, say, the ProtoBoard Wombat, meaning you can’t cut as many smaller boards out of this one – but the Wombat doesn’t have the plane. The ProtoBoard – Round 4"– ‘Stadium’ which you also asked about is obviously a different shape, but also offers 3 holes per pad, meaning you have to create fewer solder bridges/wire connections. I’m partial to 3-hole-pads myself, but in a different configuration not on offer from SparkFun – but it really tends to come down to personal preference.