Both client and principal relate to parties who require another to take certain actions or perform services in the interest of another. The difference is the relationship between the client/principal and the party ordering such actions or services.
Client is a general term for a party to a contract who orders services and pays for the services rendered. In legal context, it is often used for the entity which ordered legal services from a law firm.
Principal generally is the one who is represented by another person in a broader sense. The agent is required to act in his/her behalf. In practice, principal is used in a more restricted sense for one who appoints another to accomplish something that he/she alone is unable to.
Principal is also in a power of attorney, where the principal appoints the attorney to act in his place and stead.
