Of course, those who define capitalism and socialism differently will come to their own conclusions. Perhaps Tucker's system, with some aspects of socialism (labor theory of value) and some aspects of capitalism (pro private property and pro free market) would best be called propertarian (or individualist) mutualism.
It is not competition, but monopoly, that deprives labor of its product. Wages, inheritance, gifts, and gambling aside, every process by which we acquire wealth, rests upon a monopoly, a prohibition, a denial of liberty. Interest and rent of buildings rest on the banking monopoly, the prohibition of competition in finance, the denial of the liberty to issue currency; ground rent rests on the land monopoly, the denial of the liberty to use vacant land; profits in excess of wages rest upon the tariff and patent monopolies, the prohibition or limitation of competition in the industries and arts. - Benjamin Tucker, Why I Am An Anarchist (1892)
Other than the treatment of unused land, Tucker's economics works out in practice to the same thing as anarcho-capitalism. Whether a free market would result in zero or positive interest rates is academic. Anarcho-capitalism is essentially Spooner/Tucker anarchism updated with modern marginalist economic theory.
Tucker's theory of property did differ from Spooner's in one important regard: Tucker denied the validity of intellectual property. Tucker contended that, for something to be valid property, it had to be economically scarce. Scarcity, in this context, means exclusivity - that a good used by one person excluded it from being used in the same way at the same time by others. A bicycle or land can only be used by a limited number of people, so might be property. An idea, invention, novel or song could be used by many, at the same time, without restricting others' use, therefore it was not valid property. This validity of IP argument continues among anarcho-capitalists to this day.