Is a one cent coin a penny?

Excuse me, I'm a bit confused about something and I'd appreciate it if you could clarify for me. I've heard the term "penny" used interchangeably with "one cent coin," but I'm wondering if they're truly synonymous. Is a one cent coin indeed a penny, or are there some nuances or differences I should be aware of? I'm particularly interested in the historical context and any cultural or linguistic implications behind this terminology. Thank you in advance for your help!