Ok. so the difference is?
Drop, I can't see your attached examples, but analyze them through the following prism: it's in the name. Gari, i.e. "reap," Technically-correct, principle-driven judo reaping actions are when the foot/leg has no or very little weight on it. The whole maximum-efficiency thing.
A properly done front leg sweep, De Ashi Barai, or traditional Osoto-gari (or any of the other gari entry variations) is done as the uke's weight is stepping down into the mat but has yet to settle, or right as their leg is lifting out of the mat, in both instances, very little weight still in place with down vector, normal force/gravity combining with friction to hold foot in place on the surface.
One can, of course, blast with power through a leg with weight on it, and many, many people do and lots of them have won up to Olympic contests with this type of Osoto (Yasuhiro Yamashita, most notable... man was a beast). Still, even yamashita sensei indicates in his Fighting Spirit book that this is technically incorrect, though effective. Perfect vs. Practical, as Gerry also understands it. The below is an aargument best viewed as "Perfect is the Enemy of Good Enough."
Morote-gari is classified as a hand technique, the primary throwing is done with the hands, gripping the legs/ankles and even the heel/foot if you happen to be low enough. You don't drive the guy backwards on stopped/stuck feet, you hook & lift the legs from the position you find yourself in, thus lifting uke enough to remove his feet/legs from beneath him and he drops/falls on his back. Wrestler's shoot, football rugby tackle, you are stopping uke in his tracks, and blowing his center back off of his feet. This latter, requiring a Lot more power to function is a less-efficient physics solution. Thing is... it's way hard to do, just like taiotoshi, also a "hand technique" is taught with the leg step across to block uke's step-off of the throw... but if you ... manage ... to hit it ... just right, you don't need the leg at all. In 22 years of judo I've managed to do taitoshi without the leg and get the gake right one, single time. Planet alignment with Jupiter in Saturn's pocket or some such luck, I am certain.
But, I see what Frank was driving at, now. Dude running and swinging haymakers, and if there's any groundwork background, why not drop and fire out, tackle the guy, wrap him up in a choke or armbar and handle it that way. As long as there's only the one bad guy and you don't mind get a bit of clothing mussed up, solid solution. Personally, I'm still a fan of out of the way and send him on his...