The main difference is size. A 2 amp round pin plug is considerably smaller than a 5 amp plug, and the two are not interchangeable. It's important to check which socket you have before ordering.
2A plug: 32mm x 30mm
5A plug: 40mm x 45mm
Round pin plugs are commonly used for table lamps and floor lamps connected to a lighting circuit, allowing them to be switched on and off from a wall switch.
2 amp plugs are much less common and are often found in older installations. These days, 5 amp sockets are generally the more popular choice. In fact, at Lampfix we sell approximately 50 5 amp plugs for every 2 amp plug.
A useful tip: When choosing your plug, look at the colour of the socket insert. These are commonly black or white, so you may prefer to select a matching plug for a neater finish.