Unlike tap water or spring water, distilled water has gone through a process that strips it almost completely of all minerals. Like RO water (reverse osmosis), it is essentially pure and no longer contains any of the trace elements that would be found naturally in water. Fish kept in distilled water over a period of time may show signs of lethargy or color loss. Most aquarists choose to use tap water because it is very inexpensive and if treated with a good aquarium conditioner is safer and healthier for your fish than distilled.
If you have tested your tap water and found that it isn’t suitable for fish (extremely high or low pH for example) you could buy bottled spring water. Spring water has not gone through the distilling process and still contains the minerals bettas need. It is considerably more expensive then tap water but usually less expensive than distilled water.