The process that happens to both potato slices is called osmosis, which is a diffusion of water across the semipermeable membrane the potato slice cells possess. The water will either go into the cells, or come out of the cells, depending upon the water composition of the environment they are placed in.
The first potato slice is placed in distilled water, which is a high concentration of almost pure water, definitely higher than that which the potato's cells contain. This solution is referred to as hypotonic. The water will diffuse into the cells of the potato, causing them to swell; the cells may be characterized as being "turgid", or swollen.
The second potato slice is left open to the air. This solution, or the lack thereof, may be referred to as hypertonic, meaning the water concentration of the potato's cells is higher than that of the environment the potato is placed in. In this scenario, the water will diffuse out of the potato's cells, and evaporate into the surrounding air. The potato will assume a characteristic "flaccid" texture, because the cell membrane has separated from the protective cell wall. It will be limp, sagging, certainly without it's previous rigid structure.