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

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.
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.