A series in mathematics is where the things in a sequence are added together. One final example. My TV remote control has 37 buttons, each of which makes the TV do something different, so 37 different operations are performed. By the mathematical definition of a function, none of those 37 operations are functions. In mathematics, if you have a function and put the same thing in each time, the same thing has to come out.
People are very good at figuring out the meaning of things that are ambiguous.
Usually it will be clear whether you are using a word in its mathematical context or its normal usage. Usually the audience can fill in the missing pieces when you fail to be specific with your vocabulary. When you ask someone to rotate an object, you don't always have to specify the axis of rotation and the direction and angle through which you want the object rotated. When you write or speak you strive to transmit your ideas quickly, efficiently, and accurately. Mathematical ideas should not be an exception.