Where the impression came from — your eyes, the room, or someone's mouth
Each one below is our full write-up of that form, in the order worth reading them. Nothing is summarised — you are looking at the same pages the grammar index links to, put next to each other.
seems like, is like
V-plain / い-adj / な-adj + な / N + の + ようだ（みたい attaches plainly）
Your own judgement from direct evidence. みたいだ is the casual twin and attaches straight to a noun: 子供みたいだ.
Also used for resemblance and comparison: 雪のように白い — "white as snow".
seems, apparently; typical of
V-plain / い-adj / な-adj / N + らしい
A conclusion from what you've heard or seen around you — less committed than はず, less second-hand than 伝聞のそうだ.
After a noun it can instead mean "a proper ~": 男らしい, 春らしい日 — "a real spring day".
I hear that ~
V-plain / い-adj / な-adj + だ / N + だ + そうだ
Reporting what you were told, without judging it. Attaches to the *plain* form, which is what separates it from the looks-like そうだ.
Compare: 雨が降るそうです (I hear it'll rain) versus 雨が降りそうです (it looks like rain).