auxiliary verb, copula
it seems that; it appears that
Expresses conjecture based on direct evidence or observation. Used at sentence end; follows the attributive form of verbs/adjectives, or の after nouns.
It seems that it rained.
He appears to be tired.
auxiliary verb, copula
is like; is similar to
Indicates similarity or resemblance. Also used at sentence end; follows the attributive form of verbs/adjectives, or の after nouns.
Her smile is like a flower.
This taste is similar to chocolate.
ようだ is the complete copular expression meaning 'seems' or 'is like,' while 様 is the bare noun/suffix element used inside such patterns as のように.
ようだ is the everyday equivalent for 'seems like/similar to', while ごとき is a formal, literary word used mainly in classical or highly formal registers.
ようだ is the modern standard way to say 'like/as if', while 如し is its classical, literary equivalent found in old sayings and formal writing.
みたい is a casual, spoken way to say 'like/seems', while ようだ is the more formal, written equivalent expressing the same resemblance.
そうだ conveys hearsay based on what one has heard from others, while ようだ expresses a conjecture based on the speaker's own direct observation or senses.
ようだ expresses a subjective impression or analogy and is slightly more formal than みたいだ, while らしい is used when the judgment is based on external evidence or general expectations.
ようだ by itself expresses a direct inference ('it seems that...'), whereas ような気がする softens this into a vague personal hunch rather than a reasoned conclusion.
Derived from the noun 様 (よう, 'appearance, form') combined with the copula だ. The kanji form 様だ is rarely used in modern Japanese.