According to Prof. Wikipedia, the Equidistribution Theorem was proved by Weyl in 1910 and independently by two others around the same time.
The theorem states that for $\alpha$ irrational, the sequence $\alpha, 2\alpha, 3\alpha,..., etc. \pmod 1$ is uniformly distributed on the unit interval.
At Wolfram's MathWorld, a similar theorem is attributed to Kronecker, namely that for any irrational number $\alpha$, the sequence $\{n \alpha \}$ is dense in the unit interval, i.e., one can find a $\{k \alpha\}$ arbitrarily close to any real number b with $0 \leq b \leq 1 $. This is styled the Kronecker Approximation Theorem. Kronecker died in 1891. Note: $\{n\alpha\}$ is the fractional part of $n\alpha $.
I haven't seen a proof of Kronecker's theorem, but I have seen a proof of Weyl's Theorem. Naively (as usual), it appears the two ideas can be used interchangeably in some contexts. Even more naively, it seems there is a strong theoretical relationship between the two.
Can someone offer a thumbnail sketch of the salient differences/similarities of the two ideas (or a good reference for same)? Knowing no better, I would say Weyl owed a considerable debt to Kronecker.
Thank you.