Charging systems for ford trucks?

I have an 1987 ford F25o 3/4 tn truck , I put a new alternator on it cause I thought it was bad, still th same. When I check the the battery while its running Im getting 13.5 volts ?? Now while its running if I remove both pos and neg battery terminals by p the battery and hook my tester to the truck cables it read like it should 14.5 volts? I don't under stand it and would like to kno the solution??Help