Kosoto-gari and kosoto-gake are superficially similar techniques. I have seen many high level judoka call what I would have called -gari -gake and vice versa - what distinguishes these techniques?
Excerpt of Canonical Answer
This quotation is attributed to Kyuzo Mifune on page 162 of Kodokan Judo: Throwing Techniques by Toshiro Daigo.
Sweeping is similar to brushing an extremely light object away.
When hooking, you execute the technique as if pulling a rooted plant out from the ground.
Reaping is similar to the movement of reaping and cutting off a plant at its root with a sickle.
A kosoto gari is reap, where the side of tori's foot maintains contact with the mat. A kosoto gake is a hooking, where tori's leg bends and tori's foot comes off the mat.
As a strict classification issue, the key point is the action of tori's attacking leg. Does it leave the mat? Then it's a gake. Otherwise it's a gari.
I find kosoto gake to be most effective as a counter technique. The opponent enters for a throw where they are turning their back and standing on one leg (for example: harai goshi, hane goshi, uchi mata, ashi guruma), and you disrupt their balance and attack the far leg. As a strict Kodokan classification, this throwing action may unfortunately be classified as a harai goshi gaeshi, hane goshi gaeshi, or uchi mata gaeshi. Note that this does not apply to all throws, only these three. A counter to ashi guruma is not an ashi guruma gaeshi because this is not recognized as a distinct throw.
At the close distance for the counter and uke's weight firmly on the supporting foot, I find timing of kuzushi with the body and a strong hooking action necessary to successfully counter. For kosoto gari, the action of the hands becomes more important to break uke's balance over the heels to setup the reap.