As you noted, this has not been clear. The JOSM presets have made it a bit clearer to me.

footway is normally used for a sidewalk or dirt trail where bicycles are disallowed
path is used for everything else: paved / dirt where bicycles may also exist, specified by ‘bicycle=designated’ , ‘foot=designated’ tags.

‘track’ is most frequently used for 4-wheeled, single-vehicle width roads.