Some schools run their own nursery classes which may start 2 terms before the child is due to start school. This may account for the age4 start. Others do a year and 1 term, hence 3. Probably is a historical thing. Also the one that takes at 4 may have children starting from another nursery that does 2-4. Just go with what is best for you.
We take children from the term after they are three, meaning that we have children doing between 3 and 5 terms at nursery. The school nursery down the road takes them only for the 3 terms before they start School which means that they all have a September start. They have a much higher density of housing than us which means they can fill all their places with their September starters. We have a smaller housing stock which means that we start with low numbers in September and add to them in January and Easter.