You're both two generations from the same grandparent, so you're first cousins.
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How the terms actually work
Cousin terminology sounds complicated because it's doing two jobs at once: a degree (first, second, third cousin) and a removal (how many generations apart you are). Once you separate the two, it stops being confusing.
Degree: how many generations back you share
Count the generations from each of you back to the shared ancestor, then take the smaller number and subtract one:
- Both two generations from a shared grandparent → first cousins
- Both three generations from a shared great-grandparent → second cousins
- Both four generations from a shared great-great-grandparent → third cousins
Removed: how many generations apart you are
"Removed" shows up when the two of you are different distances from the shared ancestor. Say your grandparent is the same person as your cousin's great-grandparent: you're two generations from that ancestor, they're three. The smaller number (2) still sets the degree at first cousin, and the one-generation gap between you makes it first cousin once removed. That's the exact relationship between a first cousin and that cousin's child.
A two-generation gap is "twice removed", three is "three times removed", and so on. The removal never changes how closely related you are by blood, it just describes the generational offset.
A worked example
Your great-grandparent and someone else's great-great-grandparent are the same person. That's 3 generations for you, 4 for them. The smaller number is 3, so the degree is second cousin (3 − 1). The gap between 3 and 4 is one generation, so the full term is second cousin once removed, currently the calculator's top result above by search volume.
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