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.
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.