A masker refers to a person who is wearing a mask. This could be the case for someone who wears a mask to a party and/or social event. Wearing a mask could also be to hide one’s true identity. The goal of masking in general is to hide or alter one’s true appearance in order to present him/herself as someone or something other than him/herself.
A masquer is “a person who takes part in a masquerade or masque,” (OED). A masquerade is defined as “a riotous or extravagant assembly,” (OED). A masque is “a form of courtly dramatic entertainment, often richly symbolic, in which music and dancing played a substantial part, costumes and stage machinery tended to be elaborate, and the audience might be invited to contribute to the action or the dancing,” (OED). Someone could wear a mask to a masquerade or masque, but a masquer is not defined by wearing a mask. As you can see, a masquerade or masque is also different than just a regular party and there is more extravagance and meaning behind it.