There is no teaching job that pays for 12 months. All HS jobs for teaching pay only for the months you teach. What some schools do is to spread out the payments through the year, but the pay is the same.
That's what was meant. You can take the 9 or 12 month option. No one takes the 9 month option. I spent 5 years working for schools. I took the 12 month option. But the time off is fantastic. Nothing like the look on my wife's face when I'm not getting out of bed for three months to go slog. I miss the time off.