"suis" and "avoir" aren't similiar in the least. "avoir" refers to "verb to have" and "être" refers to "verb to be" where "suis" is a conjugation for "être". One can say "Je suis" to mean "I am". And "J'ai" to say "I have". J'ai is a conjugation for "avoir".
Hope this was helpful, but if it wasn't enough, you can always check the grammar lessons on conjugation.