Does getting fired go on your record?

I work in health care as a CNA. I got a job offer and they need me to start ASAP which won’t give me time for a 2 weeks notice. Only a 1 week notice. I live in an at will state. I have been told that if I don’t give a 2 weeks notice and go to my other job, it will be considered a termination and go on my record for other potential employers to see. Is this true?

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