The meaning of any word depends on the context.

Poached eggs is the way eggs are prepared/cooked. The verb poach also has other meanings in different contexts and yeah it could mean to illegally catch or kill an animal, as this example I found online:

<em style="color: rgb(36, 36, 36);">The two men were caught poaching lions on government land.</em>

Here is the source if you would like to read more:

<a href="https://www.google.com/amp/s/www.macmillandictionary.com/amp/dictionary/british/poach" rel="noopener noreferrer" target="_blank">https://www.google.com/amp/s/www.macmillandictionary.com/amp/dictionary/british/poach</a>;

Ougi: Yes. Boiling an egg means cooking it with its shell in boiling water.

@Mumtaz

Thank you for teaching me😆✨

Scroll down for the second set of definitions:

poach²

[ pohch ]

to cook (eggs, fish, fruits, etc.) in a hot liquid that is kept just below the boiling point.

Egg poachers: https://duckduckgo.com/?t=ffab&q=egg+poacher&ia=images&iax=images

You're looking at a different definition.

Poach: cook (an egg) without its shell in or over boiling water.