Traditionally, wakes were held at the homes of surviving family members, or some other close relative, following the death of a loved one, during which time the family would keep watch over the corpse and pray for his or her soul until the family departed for his or her burial.
Throughout the wake, relatives, friends, neighbors, coworkers and others who knew the deceased and/or the family would visit the household for many of the same reasons we attend visitations today: to pay their respects to the deceased individual and to offer comfort and support to the immediate family and to each other.
It was not uncommon (because of the 24/7 nature of wakes) for visitors to volunteer to “sit up” with the deceased during the wee hours of the night so that family members could get some sleep.
The concept of a visitation, as described above, is relatively modern and mirrored the rise and eventual prominence of undertakers, morticians and funeral directors in modern funeral/burial rites – i.e., individuals dedicated to caring for the dead and overseeing all aspects of their funeral and/or interment – which began to take hold in the late 1800s.
Wakes, on the other hand, are significantly older and pre-date the rise of Christianity. The Celts and the Anglos-Saxons held wakes, or vigils, for the dead – possibly because of the many superstitions surrounding death and corpses, and fears that “evil spirits” might take possession of the body, that existed at the time. (The popular misconception that survivors held wakes in order to make sure the individual was really dead and wouldn’t “wake up” before/after burial is probably a myth.)
Regardless, and while wakes in the traditional sense still occur worldwide, most people will understand what you mean if you refer to a visitation as a wake and vice versa.