• Basic forms
• 済む — be finished; be settled / base form
• 済みます — is finished; is settled / masu form
• 済んだ — finished; settled / ta form
• 済んで — being finished … / te form
• 済まない — not finished; not settled / negative
• 済めば — if (it) is finished / conditional
• Common expressions
• 用事が済む — an errand is done
• 支払いが済む — payment is settled
• それで済む — that will do
• More
• 済んでいる — has been settled; is done / state

済む（すむ） is a godan intransitive verb. It describes something being completed or settled naturally, without focusing on who performed the action.

• Basic forms
• 済ます — finish; settle / base form
• 済まします — finishes; settles / masu form
• 済ました — finished; settled / ta form
• 済まして — finishing … / te form
• 済まさない — do not finish / negative
• 済ませば — if (one) finishes / conditional
• Common expressions
• 仕事を済ます — finish work
• 用事を済ます — take care of business
• 手続きを済ます — complete procedures
• More
• 済ませたい — want to finish / 〜たい form
• 済ましている — has finished; has settled / state

済ます（すます） is a godan transitive verb. It means to actively bring something to completion or resolution.