Pumper Truck

what is the difference between a fire engine and a pumper?

The fire departments use the front letters to identify the trucks , example E-71: Engine 71,B71: Brush 71, P-71: Pumper 71, what is the difference between P 71 and E 71

Pumper and Engine tend to be interchangeable terms. There is really no difference between the two. Both would be capable of pumping water and carrying basic firefighting tools like hose, some ladders, possibly some water.
One possibility might be that the engine is really a quad or quint meaning that it can preform the functions of an engine company like pumping water but also has an ariel device like an extending ladder and can perform the functions of a ladder company. There are several depts in this area that have trucks that have ladders but are utilized as engine companies. If that was the case then the pumper would be just that a truck that could perform engine company duties but no ariel device.
If the dept is numbering the apparatus with the same number but changing the letter this could be a way to designate two of the same type truck with different letters. For example if station 71 has two engines, a ladder truck, a brush truck and a rescue truck, they might letter them . E-71, P-71, for the engines, L-71 for the ladder, B-71 for the brush truck and R 71 for the rescue truck.

I hope this is of some help to you.

Maxim Fire Truck Pumper Out for a joy ride