The term is ambiguous, but Merriam-Webster defines antibiotic as ...
> a substance produced by or a semisynthetic (see semisynthetic sense 1) substance derived from a microorganism and able in dilute solution to inhibit or kill another microorganism
Bacteria and fungi are microorganisms, so antibacterial and antifungal agents are all antibiotics.
Edit: OK, upon reflection, some fungi are microorganisms. Others form filaments. Candida spp. can do either, depending on growth conditions. I'm not sure about Candida auris. There are references to colonies on growth media, but that doesn't necessarily mean filaments.
I suspect the parent's confusion is due to the misapplication of antibiotics to treat viral infections (it's not really clear if viruses are alive or what, but, don't take abx for a cold please). However, as you note, antibiotics do treat other things like yeast/microorganisms in addition to bacteria. For whatever reason you'll more often see antifungals described as "antifungal agents" rather than antibiotics.
Anyhow, fungal infection is bad news, often systemic, hard to eliminate.
> a substance produced by or a semisynthetic (see semisynthetic sense 1) substance derived from a microorganism and able in dilute solution to inhibit or kill another microorganism
Bacteria and fungi are microorganisms, so antibacterial and antifungal agents are all antibiotics.
Edit: OK, upon reflection, some fungi are microorganisms. Others form filaments. Candida spp. can do either, depending on growth conditions. I'm not sure about Candida auris. There are references to colonies on growth media, but that doesn't necessarily mean filaments.