Hectic means very busy or full of activity, and often slightly exciting.(Form Lonman Advanced American Dictionary) Read more, then you can learn more different words with the same meaning.

As I see it, synonyms for the word 'hectic' are 'chaotic' or 'frenetic' and these words mean most of the time stress in your (business) life. In contrast, synonyms for the word 'busy' are 'active' or 'working' and these words I normally wouldn't use in connection with stressful activities. I'm just 'occupied' or 'unavailable'.

Hectic means very busy or or too busy. You don't say I am hectic. My life is hectic, I am having a hectic day.

I guess "hectic" is used when tasks land on your list of endless errands to be ran, and we're just on a rush to meet the deadline of completing them all. whereas "busy" is a more reasonable pace of having tasks and finishing them off. I actually face the same difficulty of using more unconventional words. This is why you find me all the time adopting a new techniques and keep on changing them constantly. One of the latest techniques is that after you finish writing an article about any thing, try to replace the words were used in it with a new ones. for instance "Mousa is good in consulting" look underneath the word. I meant what the sentence is talking about. Then you'll find I'm talking about skills. So replace the word "good" with "skillful" or maybe "masterful" can be convenient as well. after awhile it'll be a habit of you to substitute words and enhance your writing as well as your vocabulary.

Hectic is quite stressful, almost hysterical, in disorder, while busy is normal.