'Teachers' in the Bible

For even if you had ten thousand teachers in Christ, you have not more than one father: for in Christ Jesus I have given birth to you through the good news.

And God has put some in the church, first, Apostles; second, prophets; third, teachers; then those with wonder-working powers, then those with the power of taking away disease, helpers, wise guides, users of strange tongues.

Are all Apostles? are all prophets? are all teachers? have all the power of working wonders?