1st/2nd/3rd/etc. are counting back to a common ancestor, starting with your grandparent. If you share a grandparent, you’re first cousins. Each great adds a number, so # of greats + 1 that you both share.
“Removed* is that cousin’s children. My second cousin’s child is my second cousin once removed. Their grandchild is my second cousin twice removed and so on.
So, to answer you directly: you and your second cousin share a great grandparent. Your grandparent is your first cousin once removed’s *great* grandparent.
Your first cousin is the child of your aunt or uncle.
Your first cousin once removed is a person who is the first cousin of one of your parents. (They are ‘once removed’ because you are separated by 1 generation-level from being first cousins.)
If your first cousin once removed had a child, that kid would be your second cousin because you’d both be on the same generational-level (with your parents being first cousins).
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