Can it be called an affair if it was just a one-night stand?
When most couples marry or commit to each other, there is a mutual understanding (usually in the form of a vow) that certain connections outside the relationship will be out of bounds. This includes both physical and emotional connections. When someone violates these boundaries, they break their promise and betray their partner.
Once you become intimately involved with another person (whether emotionally or physically or both, whether once or many times, whether for a short or a long time), you have damaged the underlying trust in your relationship. Your definition of an affair might describe an ongoing relationship instead of a brief encounter, but now is not the time to debate word meanings. If your partner calls it an affair, deal with it like an affair and work toward healing.