In lang=en terms the difference between stumble and slide
is that
stumble is to cause to stumble or trip while
slide is to pass along smoothly or unobservedly; to move gently onward without friction or hindrance.
As nouns the difference between stumble and slide
is that
stumble is a fall, trip or substantial misstep while
slide is an item of play equipment that children can climb up and then slide down again.
As verbs the difference between stumble and slide
is that
stumble is to trip or fall; to walk clumsily while
slide is (ergative) to (cause to) move in continuous contact with a surface.