の様(よう)にLike (Noun), Similar to (Noun)

のように・のような and そう both express impressions, but with different nuance. のように・のような show direct comparison, like 'like' or 'as if,' e.g. 春のように暖かい ('It's warm like spring.'). そう expresses a perceived impression based on observation, e.g. 暖かそう ('It seems warm.').

のように・のような and みたいに・みたいな both express comparisons, 'like' or 'similar to,' but differ in formality and structure. みたい is more casual and attaches directly after nouns, e.g. 春みたいな天気 'spring-like weather'. よう is more formal and uses の before it, e.g. 春のような天気, which has the same meaning.

Both そうに・そうな and のように・のような describe appearances, but with different nuances. そうに・そうな conveys a subjective impression or an event that seems about to happen, e.g. 優しそうな目 'kind-seeming eyes' or 雨が降りそうな天気 'weather that seems like it's about to rain'. ように・ような, in contrast, expresses comparison, e.g. 春のような天気 'spring-like weather'.

のように・のような and ふうに both express similarity, but with different usage and nuance. のように・のような follows nouns, e.g. 春のような天気 'spring-like weather', and expresses a general comparison. ふうに, on the other hand, typically follows verbs or words like こんな and そんな, implying 'in a way' or 'giving the feel of,' e.g. こんなふうに話す 'to speak in this way'.

Both のように・のような and ように・ような use よう to express similarity, but with different structures and uses. のように・のような follows nouns for comparisons, e.g. 日本人のような話し方 'a manner of speaking like a Japanese person's'. ように・ような follows verbs and conveys the meaning of doing something 'as if' or 'in a way that is like,' e.g. 日本人が話すように話す 'to speak like a Japanese person speaks'.

Both のように・のような and にみえる express how something 'appears,' but with different nuances. のように・のような is used for comparisons and connects to nouns or the rest of the sentence, e.g. 春のような天気 'spring-like weather'. にみえる specifically refers to visual appearance and can be used alone, e.g. その虫は葉っぱに見える ('That bug looks like a leaf.').