is not merely the difference between “a nightcap” and “drinking your breakfast” although it may as well be.
from what i can tell, traditionally an apéritif is more likely a cocktail or a light wine, on the principle that you want something to want something to stimulate both your appetite and taste buds, thus not too sweet or alcoholic.
a digestif, to be taken after the meal, is supposed to settle and satisfy, and so tends to include higher alcohol, often sweeter, drinks – like port or cognac – or herb infused, bitter or syrupy liqueurs. and not that you can count on this – because it is a quality that arises from a delicate interplay of custom, affectation, and the inherent qualities of the drink itself – but think of a digestif as something you intend to linger over, in a state of chymifying repose, as the name implies.
this clearly is not hard and fast, however, since fortified wines are as often taken as apéritifs as they are digestifs, and pastis is pretty common as an afternoon kind of drink, for example. i personally enjoy bitters pre-dinner because it feels like bitterness, like astringency, gets the juices flowing an prepares the ground (uh, the ground of the gut) for the forthcoming meal. thus it is not so much that certain boozes “are” one or the other, but are referred to as such on temporal – as opposed to strictly qualitative – grounds. that some drinks are traditionally in one class more than another may be taken as loosely instructive, but don’t lose your cool over it.
similarly, is there ever a bad time for a bloody mary?