Doilies were originally used to separate the desert plate from the finer bowl at a formal dinner and even to decorate a plate being used to serve pastries and desserts. Later doilies became more widely used by everyday folk to protect fine wood furniture from being scratched when serving dishes were used and against water damage from wet glasses and the like. They're most commonly crocheted so the beauty of the furniture on which it sits can be seen through it. It was customary for the lady of the house to make her own in order to show off her handiwork.
Antimacassars are also commonly crocheted or made of linen and are used to protect upholstered furniture. In the 19th century men used macassar oil to achieve that dandy, well polished look men of the period enjoyed flaunting. However, the oil was dreadfully damaging to fabrics on the backs of chairs where their heads rested, so the ANTImacassar was placed on the chair back to protect it. Similarly, arm covers protect the arms of the chair against staining by dirty hands and forearms.
A crocheted piece that's round is a doily and thus used on the dining room table or buffet/server. A square or rectangular piece, especially if it's much larger than needed for a bowl or serving dish, is more likely an antimacassar. Small rectangular pieces are more often armchair covers.
My grandfather was a farmer and then a farm machinery mechanic, so my Grandma always had an antimacassar and arm covers on the furniture where he would most commonly sit.