そうだ
souda
The two そうだ are one thing: "this isn't mine"
The picture You didn't verify it. You picked it off the surface with your eyes, or off the air with your ears, and you set it down exactly as you found it. そうだ sets down what you picked up outside, untouched; ようだ is the conclusion you drew after lining those pieces up yourself.
Where the picture shows up in そうだ
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picked up by eye
雨が降りそうですね。
ame ga furisō desu ne
Looks like it's going to rain.
Your eyes sweep the underside of a low, heavy cloud and set down exactly what they saw.
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the surface, before the taste
このケーキ、おいしそう。
kono kēki, oishisō
That cake looks delicious.
Before the fork ever touches it, your eyes scoop up the glossy surface of the cake.
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someone else's outside
課長、今日は忙しそうです。
kachō, kyō wa isogashisō desu
The section chief looks busy today.
From the doorway you watch the section chief buried in paperwork — only the outside of him.
You can't see inside another person, so 忙しそう, not 忙しい.
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picked up by ear
田中さん、来月辞めるそうです。
tanaka-san, raigetsu yameru sō desu
I hear Tanaka is quitting next month.
A remark drifts over from the next desk; your ear catches it and hands it on untouched.
降りそう (surface) attaches to the ます-stem; 降るそう (hearsay) attaches to the plain form. The shape tells you which.
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passing it on with its source
天気予報では明日は雪だそうです。
tenki yohō de wa ashita wa yuki da sō desu
The forecast says snow tomorrow.
You lift the snow icon straight off the forecast screen and set it down in front of the other person.
After a noun it's だそう — never 雪そう.
All of it in one picture
There are not two そうだ. Pick the sky's surface up with your eyes and you get 降りそう; pick up the cake's surface and it is おいしそう; pick up the outside of another person and it is 忙しそう. Pick something up with your ear and it is 辞めるそう, and carry the whole forecast across and it is 雪だそう. Only the joint changes — ます-stem or plain form — while the job stays the same: set down what you collected outside, without touching it.