I believe there is a difference you could make.. Classics are overall iconic, they are admired and loved by the gp. Cults are like a subcategory, they have a smaller and very specific (target) audience (eg geeks, teenage girls, feminists, gays,...) but these "cult classics" are admired by that audience and very iconic to them.
Of course there are cults that become classics because of their large following and eventually become more appealing to the gp like Star Wars, Buffy, Mean Girls,... Idk just my opinion but there are probably some better/official definitions on the web
EDIT: To add on to why some fade and some become big, it's simple what's iconic to one generation isn't necessarily considered iconic by another.. so some are forgotten and others get an unexpected following (mainly because of the internet nowadays) however some classics and cults remain untouched and are considered iconic by all generations
