Cut up a mushroom and you’ll see that it is made of the same type of cell as mycelium: hyphae.
It sounds like you are describing the differences between plant and fungal cells. Grapes and woody grape vines are both made up of plant cells, which are a type of cell found in all plants. Plant cells have a cell wall that provides structural support, and they also contain chloroplasts, which are organelles that are responsible for photosynthesis. In contrast, mushrooms are made up of fungal cells, which are a type of cell found in all fungi. Fungal cells do not have a cell wall and do not contain chloroplasts. Instead, they have a cell membrane and a nucleus, which are also found in plant and animal cells.
