Conflicting Read & Write permissions on Mac external hard drive

As you see by this screenshot, my external hard drive is giving me contradictory information.

It tells me that my account should be able to "Read & Write" but then also above it says "You can only read"

Am I somehow on an account that is not the main one with my name?

Or is this just how Mac's treat externals?

I searched this topic from a few places and everything just said to re-format it or something of that variety. Is that really my only option when it tells me that I should be able to also write on the drive?

[Re-Titled by Moderator]