Earphones/earbuds are those worn in the ears without a headband. While they come in pairs, one can have an earphone/earbud in one ear, leaving the other dangling.
Some, but not all, headphones have a band. The earphones or earcups (you may not find this in the dictionary) that make up the pair are worn over or on the ears. Thus, one can wear headphones with only one earcup/earphone on.
Your example could be correctly written in a number of equivalent ways:
- She wore an earphone in one ear and listened to him with the other.
- She had headphones on with an earcup slid off so she could also listen to him.
- She left an earbud in one ear and listened to him with the other.
- She wore headphones but had only one ear covered while she listened to him with the other.
- She wore headphones with only one earcup on, and listened to him with the other ear.
- She wore headphones with a cup over one ear and listened to him with the other.
Once the word earphone is used, it is implied that it is present in a pair or set of earphones/headphones, with only a very few exceptions.