Humans have more than 5 senses; we have 5 traditional senses, but over 20 senses in total with non-traditional senses counted. Other organisms have a variety of senses too.
Fungi are one of the kingdoms of Eukaryote. The fruiting part of the of the fungi is called a mushroom. Fungi fertilize the ground so plants can grow, considering plants are responsible for the oxygen on earth this is important.
All mushrooms are fungi, but not all fungi are mushrooms. Mushrooms are the fruiting body of fungi that typically grow above ground.
A truffle can generally be considered a type of mushroom under a definition that considers any spore bearing fruiting body of a fungi a mushroom.