This is going to be another case of one word meaning different things to different people. Anyone in a traditional monogamous relationship certainly will view sexual exclusivity as one of the biggest factors in determining if you are a) Committed b) having fidelity
In modern human relationships, the term can refer to sexual monogamy. In western culture this often means adherence to marriage vows, or of promises of exclusivity or monogamy, and an absence of adultery. However, some people do not equate fidelity in personal relationships with sexual or emotional monogamy. (For example, see polyamory and Open marriage.)
Again...people have different views. Each group/individual is allowed to use the words however they chose...they're just words.