An apostate is one who had the faith and departs from it. A person teaching heresy is one who is still in the faith and teaches a doctrine that doesn't coincide with the traditional norm. An apostate will deny the Trinity, the resurrection and virgin birth, the Bible as the Word of God, etc. A person teaching heresy may teach that we must worship on the traditional Sabbath or that we can't have music in our worship services.
Heresy is generally a doctrine someone else holds in relation to what your specific church tradition teaches . Both parties will say they teach from the Bible and it is the standard but the interpretation is different. I think Christians are very quick to label someone as teaching heresy or an apostate teacher just because the person doesn't teach exactly what the other person thinks the Bible says it teaches. Discernment is a requirement and a thorough understanding of the Word of God is necessary before we start putting labels on folks. What you may consider heresy may in fact not be. We must rightly divide the word of truth. And just because something or some approach makes us uncomfortable and is outside of our traditional norm doesn't make it heresy or the person an apostate. Take it to the scriptures as the Bereans did.