Maximum number of vertices in undirected graph
Kruskal's algorithm is only applied to connected graphs. These have at least $|V|-1$ edges. On the other hand, the complete graph has $\binom{|V|}{2}$ edges, and so
$$
|V|-1 \leq |E| \leq \binom{|V|}{2}.
$$
The left-hand side is $\Omega(|V|)$ and the right-hand side is $O(|V|^2)$. Therefore $\log |E| = \Theta(\log |V|)$. For this reason, the two quoted running times $O(|E| \log |E|)$ and $O(|E| \log |V|)$ are completely identical &mdash; on connected graphs, an algorithm has running time $O(|E| \log |E|)$ iff it has running time $O(|E| \log |V|)$.