As we know, mathematicians like to avoid the term "groupoid" to refer to a set with binary operation. This term, as we know, originates from the works of Brandt, so called Brandt groupoid. A Brandt groupoid is a groupoid in the sense of category theory, however for some (unknown to me) reason in history the term began to also be the name for a set with binary operation.
For the historical reasons, and the fact that the term is somewhat ambiguous, I saw a lot of people prefer the term "magma".
However, there is another side of the argument, and that is, what do people that actually work in the field call their objects? Is it magma, groupoid, or maybe something else entirely? In some fields, like quasigroup or semigroup theory, I saw a lot of people refer to those objects as groupoids. Is this possible that researchers actually prefer the term groupoid in their work?
References:
"The Algebraic Theory of Semigroups" A. H. Clifford, G. B. Preston
"Elements of Quasigroup Theory and Applications" V. Shcherbacov
"Universal Algebra" S. Burris, H. P. Sankappanavar
Speaking as a quasigroup theorist, I can say that it is definitely true that even today more people in the area use "groupoid" in the Hausmann-Ore sense (set with binary operation) than in the categorical sense. A lot of the preference is both geographically and generationally based. For instance, that usage is prevalent among older quasigroup theorists from former Eastern Bloc countries.
In semigroup theory (my other area of interest), "groupoid" is usually meant in the categorical sense, because the notion is heavily used in the theory of inverse semigroups. However, many semigroup theory papers treat groupoids as algebraic structures with a partially defined operation rather than as a special kind of category.