Those are not inherently the same,
Yes, they are, like I said, you don't have to mean it to be transphobic for it to be transphobic. People who are ignorant and get called out who don't want to be transphobes will admit ignorance, apologise, and improve their behaviour. Anything else makes a person a transphobe, no matter how uncomfortable that makes you.
This is transphobia since it is factually incorrect and stems from wilful ignorance, and I'm shutting it, and your tone policing, down. There, how's that?