I'm heading to means that you are going somewhere, and it is followed by a place. For example., I'm heading to the store. I'm heading to the grocery. I'm heading to the gym. I can't, because I have to head to work in a little bit. I'm heading out means that you're ready to leave a social engagement. We say, alright guys, I'm heading out. It means, I've had enough and I'm heading back home.

Наталья, вот ещё одно объяснение от носителя английского языка (не меня): https://www.youtube.com/watch?v=spI_WyGtS7k. Видео идёт на русском языке, поэтому не бойтесь, что вы что-то не поймёте.

Heading as a noun is a nautical term for "direction." Heading as a verb is a synonym for "going."

it means 'going towards/in that direction'.