na-adjective
similar; alike; in the same way
Describes things that are alike in appearance, nature, or manner. Often used as 同じような or 同じように.
彼は父親と同じような顔をしている。
He has a face similar to his father's.
同じようにやってみてください。
Please try doing it in the same way.
似ている is a verb meaning 'to resemble', while 同じよう is an adjectival noun meaning 'similar' and often modifies nouns or verbs.
同様 is a more formal, Sino-Japanese equivalent of 同じよう, often used in written or official contexts.
Compound of 同じ (same) and よう (appearance, way). The exact historical derivation is straightforward; よう is often written in kana in modern usage.