• Basic forms
• 残る — to remain; be left / base form
• 残ります — remains / masu form
• 残った — remained; was left / ta form
• 残って — remaining / te-form
• 残らない — does not remain / negative
• 残れば — if it remains / conditional
• 残れ — remain! (rare) / imperative
• Common expressions
• 時間が残る — time remains
• 印象が残る — leave an impression (lit. remains)

残る（のこる） is an intransitive godan verb. It describes something staying behind naturally, without intentional action.

• Basic forms
• 残す — to leave; save; preserve / base form
• 残します — leave; save / masu form
• 残した — left; saved / ta form
• 残して — leave and … / te-form
• 残さない — do not leave / negative
• 残せば — if (you) leave / conditional
• 残せ — leave it! / imperative
• Common expressions
• 料理を残す — leave food
• 記録を残す — leave a record
• More
• 残せる — can leave / potential

残す（のこす） is a transitive godan verb. You intentionally leave something behind — the transitive partner of 残る.