Good question. While there are no hard-and-fast definitions, in general a serum is chemically different than a cream, lotion, balm or oil type of "emulsion" (a mixture of non-mixable components). Primarily, the difference involves the use -- or lack thereof -- of an emulsifier. Creams and lotions generally contain lipophilic (fat-loving/fat-soluble) ingredients which need an emulsifier to blend with hydrophilic (water-loving/water-soluble) ingredients. Often, ten times the amount of emulsifier is needed to go along with a fat-soluble ingredient, just to get it to blend.
By comparison, a serum doesn't contain many emulsifiers, or sometimes none at all. This leaves room for more potent, active ingredient percentages, so serums are almost always more powerful and concentrated than other types of emulsions. Typically, the active ingredients in a serum have a smaller molecular size than a lotion or cream so penetrate the skin faster, and deeper. Because the percentage of active ingredients is usually much more than in a cream, serums usually cost more, but of course can be much more effective.