both 摇and晃 can be an action of a person -----shake down fruit from a tree; 晃落树上的水果// row a boat; 摇船 but 晃 can also be an action of an Inanimate subject, -------- like tree's branch: Branches sway gently in the wind. 树枝在风中微微晃动. of course if you just want to say 树枝在风中微微摇动， it won't be a grammar error at all, but it's not the most common expression. ps, 晃have two pronunciations one is /huàng/ , it is a verb, as we mentioned in this question. the other is /huǎng/ , 动词 1. （光芒闪耀） dazzle: dazzlingly bright; 亮得晃眼 a shining bayonet 明晃晃的刺刀 2. （很快地闪过） flash past: A figure flashed past the window. 窗外有个人影儿一晃就不见了。 A fortnight passed in a flash. 一晃半个月过去了。

摇：To move an object back and forth 晃：To shake; swing

They have little difference.Both of then express the same meaning.We can say 摇摇晃晃，摇头晃脑.