A valid route and a shortest route are different claims
A valid route uses accepted words and changes exactly one letter at each step. A shortest route adds another claim: no valid route reaches the target in fewer moves. Checking one sequence proves the first claim, but it cannot by itself prove the second.
That distinction matters when a page calls an answer optimal. The result must come from a search over a specified word list, or another method that actually rules out shorter routes.
Imagine words connected by lines
Picture every accepted four-letter word as a dot. Draw a line between two dots when their words differ in one position. A word ladder follows these lines from the starting word to POOP. The problem is to cross as few lines as possible.
This picture also explains dead ends. A perfectly ordinary word may have few useful neighbors in the chosen list. Familiarity alone does not make it a convenient stepping stone.
Search one distance at a time
Breadth-first search checks all words reachable in one move, then all words reachable in two moves, and so on. Because every legal transition costs one move, the first distance at which it reaches POOP is the minimum distance in that word list.
A careful implementation remembers visited words, so it does not waste time repeatedly exploring the same position. If it exhausts every reachable word without finding POOP, there is no route in that particular list.
Several routes can share first place
A puzzle does not need one unique shortest answer. Two branches may reach the same word after the same number of moves, or remain separate until the target. Both complete routes can be equally short.
Finding every tied route takes extra bookkeeping: the search must retain all predecessors that reach a word at the best distance. A display may show only a sample when there are many, but it should clearly distinguish that sample from a complete list.
The word list sets the boundary
Adding an accepted word can create a shortcut; removing one can make a route longer or disconnect it entirely. Therefore, shortest always means shortest under the stated rules and vocabulary. A solver can be mathematically correct and still disagree with a game that uses different words.
When comparing answers, check the word-list information before comparing move counts. A useful result shows the route, lets you inspect each transition, and explains any limits on compatibility or the number of displayed alternatives.