Could you please justify the title of the story " A Fishy Story" by Jerome Klapka Jerome? Does the word "Fishy" have a pun?

"A Fishy Story" is a story about the narrator and his
friend, staying in an inn. In the lobby, they find a trout placed in a glass case over
the wardrobe. They find many people, claiming that they had caught the
trout. It filled the two with laughter, and a bit of suspense as well.
They tried to get hold of the trout, but fumble, and drop it down. It broke into several
pieces. They found it absurd how a stuffed trout could break; then they realise that it
was made up of Plaster of Paris.

There is a pun intended on
the word "Fishy". Firstly, it refers to the FISH itself. At
the same time, it refers to the aroma of curiosity and
suspense created.