Confused to determine first cousin and second cousin

First cousins will have a common grandparent. Second cousins will have a common great grandparent. Third cousins will have a common great-great-grandparent. Your great grand mother's brother's son will be your uncle if you see the relation.
But you will be second cousins only not first cousins. Second Cousins will not have any common grandparent. So they can marry and it will be legal only in India.

First of all, you take a firm decision between which cousins you want to get married and that will determine the right answer from the spectre of advisors here. Because our advice is purely on legality and your liking of any cousin is very personal and that should not clash here.

1. You are second cousins as your great-grandfather is common.

2. The marriage between second cousins have no problem from legal point of view.

3. However, the legal issue is not everything in Indian marriages. You have to check the opinions of the elders of both sides.

Thank you all for sharing such valuable information.
I also want to add that my mother's mother (grandmother) have 2 brothers. One of them married my Aunt ( my mother's younger sister). My aunt is a second wife. He married my Aunt without the consent of his first wife (alive). Since my aunt is married to my grandma's second brother, is it legal to marry my grandmother's first brother son. My mother's father's parents and my cousin's father's mother's parents are our common great grandparents.

1)Yes, you are the second cousin in the sense that your great grand father is common.
2) Now in order to have the marriage negotiation with your second cousin, such a a marriage is not permissible since both of you belong to the relationship of brother and sister. This is as per Hindu - mythology and as such negotiation of such marriages are forebidden.
3) if at all, both of you are ready for the culmination of marriage, you need to approach the court and the marriage can be solmenised with the permission of the court. You may invite the notable citizens of your locality.

As you share the common great grandparents between you it is the second cousin relationship from your mothers side. This relationship is acceptable for marriage in most of the countries including India.

First cousin marriages are not allowed in Hindu community as per Hindu Marriage Act, 1955 and all kinds of such first cousin marriages are illegal. At the same time there is no problem for second cousin level marriages and these are accepted legally. In some places some elders do not recommend for close quarter marriages due to some beliefs related to medical problems but scientifically talking that is not so severe a factor. The genetic scientist give the gene sharing probability as about 6% in case of second cousin marriages and about 3% in case of third cousin marriages.