nLab
1-groupoid

Fix a meaning of $\mathrm{\infty }$-groupoid, however weak or strict you wish. Then a $1$-groupoid is an $\mathrm{\infty }$-groupoid such that all parallel pairs of $j$-morphisms are equivalent for $j\ge 2$. Thus, up to equivalence, there is no point in mentioning anything beyond $1$-morphisms, except whether two given parallel $1$-morphisms are equivalent. If you rephrase equivalence of $1$-morphisms as equality, which gives the same result up to equivalence, then all that is left in this definition is a groupoid. Thus one may also say that a $1$-groupoid is simply a groupoid.

The point of all this is simply to fill in the general concept of $n$-groupoid; nobody thinks of $1$-groupoids as a concept in their own right except simply as groupoids. Compare $1$-category and $1$-poset, which are defined on the same basis.