The same pair, two different calculations
Feeding (1,2,3) and (4,5,6) into the dot product calculator gives 32 (with a 12.9332° angle between them); feeding the identical pair into the cross product calculator gives the vector (−3, 6, −3), with a magnitude of 7.348469. Same two inputs, two calculators, two answers that don't even share a type — one's a number, the other's a vector.
What each number actually answers
The dot product answers "how aligned are these vectors," compressed into one signed number — larger and positive means more aligned, zero means perpendicular, negative means pointing broadly apart. The cross product answers a completely different question: "what vector is perpendicular to both, and how much area do they span together" — its magnitude (7.348469 here) is the area of the parallelogram the two vectors form.
The tell: parallel vectors
Parallel vectors make the contrast obvious. (2,4,6) and (1,2,3) point in exactly the same direction (one is just double the other), giving a dot product of 28 and an angle of exactly 0° — fully aligned. Their cross product, however, is (0, 0, 0) — a zero vector, with zero magnitude. Parallel vectors span no area at all, so the cross product correctly reports nothing, even while the dot product reports a substantial positive number.
Why both exist as separate calculators
Because they measure unrelated properties, no single formula could replace both: physics problems involving work or projected length need the dot product's scalar; problems involving torque, angular momentum, or a surface normal need the cross product's perpendicular vector. Running the same two vectors through both is a legitimate way to get a complete picture — alignment from one, perpendicular spread from the other — not redundant double-checking of the same fact.