This is a good question. I used to be in the fruit trade and thirty-ficve years ago tangarines and mandarines were the main varieties of what is called 'easy peelers'. The difference between them is in skin colour, shape, flavour and the number of pips. Mandarines are flatter, paler and have a subtle orange flavour. They also contain quite a lot of pips. Tangarines are brighter in colour, sweeter and have fewer pips.
Satsumas were introduced to meet the demand for seedless, easy to peel citrus fruit (we are so bloody lazy in the west). Satsuams are much lighter in weight than mandarines or tangarines, have a pale skin and are usually seedless. They are cheap and easy to grow and because of mass planting, they can virtually be eaten all year round.
Clementines have been around for centuries but production of them was increased dramatically when it was noticed that they are sweet, easy to peel and seedless! Mass planting of both clementines and satsumas has resulted in many hybrid breeds that do not have a consistent flavour or reliability in tems of being seedless and easy to peel.
You can get mandarines and tangarines in the winter months if you look out for them and they tend to fill the gap when there are fewer 'easy peel' citrus fruits around in the summer.