And so, Paul is saying, "Look, if anyone teaches differently, that's the mark...that's how you know them." It is, first of all then, what they affirm. You have to listen to what they say. Is it different than what you know Scripture says?
Are they saying something different? The word is heteros didaskalia, a heterodox teaching rather than an orthodox teaching. That means a heresy, a false teaching, something that is different than the Scripture teaches. They don't get their teaching out of the Word of God, they have something different than the Bible, some vision, some revelation, some psychological insight, some self‑generated, self‑spawned doctrine, some interpretation that is contrary to Scripture. Anything different than the sound true teaching of the Word of God revealed marks a false teacher. It could be a teaching that denies that God is the only true God. It could be a teaching that denies that God is a spirit and turns God into an idol or a man. It could be a teaching that denies that God is a trinity or that denies some of the attributes or any of the attributes of God. It could be a teaching that denies that God is almighty, that God is sovereign, that God is the creator, that God has revealed Himself in history. It can be a teaching that denies His person, His attributes or His works. And any such thing marks out one who has a virus that is deadly.
It could be error about Christ, error about His lineage, error about His virgin birth. Someone who teaches contrary to the sinless perfection of Christ, contrary to His substitutionary atoning death on the cross, contrary to His resurrection, contrary to His miraculous life and works, His perfect teaching, His Second Coming, His high priestly ministry of intercession, His eternal reign, any of that. Anyone who teaches differently than that. It could be a denial of the authenticity of Scripture, the inspiration of Scripture, the authority of Scripture, the inerrancy of Scripture. It could be a denial of the work and ministry and person of the Holy Spirit as revealed on the pages of holy Scripture.
Any deviation from what the Bible teaches marks out the virus of false teaching that can deadly...in a deadly way infect people. Any area of truth twisted, perverted or superseding Scripture is cause for us to take note.
~John MacArthur on "The Pathology of False Teachers"
I would add that what some false teachers OMIT is also heresy. Additionally, claiming right doctrine in area, but then contradicting it or sliding in an exception (via "ignorance" for example) is also false teaching.
As Robert Morey so astutely said,