I heard that mushrooms aren't plants per say... They still look very vegetal to me, can you help me understand?
It depends on your personal definition of mushrooms.
As it is usual for any science, there are many exceptions to the following rules, with plants exhibiting one or more structures or elements that should belong in a fungus or vice versa, usually an evolutionary tree will tend to place a given species as either a plant or a fungus with parallel evolution or symbiosis or parasitism muddying the clear lines.
But on average it can be said that:
• If you consider mushrooms to be the stalk with the hat and nothing else, then those are most similar in purpose to fruits of the actual fungus, which is usually underground, and is most similar to molds.
• The fungus itself usually has a cellular structure vaguely similar to plants, but uses chitin instead of cellulose as the barrier between cells.
• A fungus usually does not rely on chlorophyll or other means to produce its own food from raw ingredients, but processes existing food via digestion.
• A fungus usually uses spores to reproduce, instead of having specialized structures like seeds and pollen.
• Finally a fungus normally stores food via Glycogen, while plants normally use Starch.
Can you explain what glycogen and starch are, and why fungi and plants use different forms for storage?
Sure! 

Glycogen and starch are both types of polysaccharides, which are long chains of sugar molecules. Glycogen is the form of glucose storage in animals, while starch is the form of glucose storage in plants.

Fungi, on the other hand, can use both forms of glucose storage depending on the species. Some fungi store glucose as glycogen, while others store it as starch.

The reason why plants and fungi use different forms of glucose storage likely has to do with their evolutionary histories and the specific needs of their respective lifestyles. Plants are sessile organisms that rely on starch as a long-term energy reserve to support growth and reproduction. Fungi, on the other hand, are heterotrophic organisms that obtain nutrients from a variety of sources, including dead organic matter. This flexibility may allow them to use either glycogen or starch depending on their environmental conditions and nutrient availability.

Overall, the different forms of glucose storage used by fungi and plants likely reflect adaptations to their unique lifestyles and nutritional requirements.