One version of the Pigeonhole principle says that if the cardinality of a set $A$ is greater than that of a set $B$, then there can be no one-to-one function that maps from $A$ to $B$.
Another version says: If $n$ elements are partitioned into $m$ subsets, then at least one subset must contain at least $\lceil n/m \rceil$ elements. Note that the $\lceil \ \rceil$ enclosing the $n/m$ tells us to round the value up.
The latter version is just a more powerful version, no? It seems strange to me that one version of a theorem can objectively give more information than another, so it's likely that either the latter version is not correct or I am incorrect in thinking that it somehow has more utility.
Or is this normal? Is it common for certain versions of theorems to simply have less utility than other versions?