You don't normally see fungus growing on clay pots unless it is in a greenhouse with a high humidity. Then you see algae and green slimy growths.
However you can see a white powdery exudate on clay pots where the local water has a lot of dissolved salts. If your area has a lot of limestone this will likely be calcium and a mix of other salts. If this is what you have it would be dry to touch, whitish and some can be scraped off with a knife or other hard surface.
To remove take off as much as you can with a wire brush and then apply linseed oil, which will make the powdery deposits invisible. I use over strength vinegar, or a 10% solution of hydrochloric acid. Rinse well afterward. When using hydrochloric acid wear goggles, long sleeves and gloves!