I don't understand your question, Tom. Avoir means "to have". It is used in many different contexts in French, in particular as auxiliary verb in forming other tenses. In this respect it is similar to English.
By "suis" do you mean the verb être ("to be")? It is similarly used to form tenses and is also an irregular verb whose conjugation is important to know well.
"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.
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