The test: does every random integer fall inside the range?
Using that same minimum of 1 and maximum of 20, the random integer generator was called ten times in a row, producing 11, 19, 6, 13, 18, 9, 12, 6, 10, 6. Checking each one against the 1-to-20 bounds: every single value is at least 1 and at most 20, so all ten draws pass. That is the real, checkable relationship between the two calculators — the random integer generator's single draw is always a member of the same pool of whole numbers (1 through 20) that the number range generator shuffles and samples from when given identical bounds. The five specific numbers the range generator happened to pick — 3, 8, 9, 17, 18 — are just one possible sample from that pool; the random integer generator's ten draws are ten more independent samples from the same pool, and none of them could ever be 0 or 21 no matter how many times you run it.
Why the specific numbers differ but the bounds don't
None of the ten random integer draws (11, 19, 6, 13, 18, 9, 12, 6, 10, 6) exactly match the five numbers the range generator selected (3, 8, 9, 17, 18), and that's expected rather than a problem — both calculators call the same kind of random draw underneath, so two separate runs, even with identical bounds, are not required to overlap at all. Every fresh run of either calculator draws new values from Math.random(), so re-running this exact comparison will not reproduce these exact numbers. What stays fixed and reproducible is only the bounds themselves: set minimum to 1 and maximum to 20 in either calculator, and every number either one returns is guaranteed to be a whole number from 1 to 20.
Why this invariant is useful to know
Understanding that both calculators draw from the same underlying pool for a given range makes it possible to use them together with confidence — for example, generating a list of 20 raffle ticket numbers with the number range generator (1 to 20, duplicates off) and then separately using the random integer generator with the same 1-to-20 bounds to pick a single "bonus" number, knowing that bonus number is guaranteed to belong to the same set of possible ticket numbers even though it was drawn independently and could coincide with one already issued.