Posterior tibial tendonitis in my left foot. my question is, is posterior tibial tendon dysfunction the same condition just different names?

Different: Tendonitis means pain and inflammation. Dysfunction means that it is not working properly such as being torn or overstretched. Tendonitis may lead to dysfunction.

They are related: Tendinitis is an inflammation that may or may not result from the posterior tendon dysfunction. The ptd can easily result from the painful tendinitis as well.