Terminology can be confusing. Genealogy classifies family relations based on generation, following direct descendants and immediate in-law relationships. When you share an ancestor you are related by blood to another person. Thus you can trace your lineage by child relationships back to a specific ancestor, a direct descendant.
As such your generation line is you, your siblings, and your cousins (1st, 2nd, 3rd, etc.).
Your first cousins share the same grandparents as you.
Your second cousins share the same great-grandparents.
Your third cousins share the same great-great-grandparents, and so on.
The generation directly above you and below you is cousins once removed. They are separated by one generation. This would be the generation of your children and your parents generation lines.
Your first cousin once removed is separated by one generation and shares the same grandparent.
Your second cousin once removed is separated by one generation and shares the same great-grandparent.
The generation above or below after that is twice removed, they are two generations apart from you. This would be your grandchildren and grandparents generation lines.
Your first cousin twice removed is separated by two generations from you and shares the same grandparent.
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