In essence a shower bath is simply any bath that has a shower over it. However, some baths are made specifically for this purpose and come with certain features.
The first thing to consider is that you can’t, or at least shouldn’t, stand up to shower in the sloped end of a bath. The standing position is too far forward and the temptation is to step back which will be onto a slippery, sloped surface!
The bath should have an edge which is flat and wide enough to have a shower screen fitted (unless you are using a curtain).
Some baths are marketed specifically as shower baths and these are generally called P-Shaped baths or L-Shaped baths, they are named as such as the shower end of the bath is wider than the sloped/non showering end. This is either curved to make a P-Shape, or squared off to make an L-Shape.
These are clever designs as they provide much more room for you to stand and shower in, usually have a screen the same shape as the bath, but don’t require the depth to be the full length of the bath.
A common size for a bath such as this would be 1700mm long and 700mm at the bath end and 850mm at the showering end.