If a group and a groupoid have the same profinite completions, can anything be said about them?

Question

Pretty much what I ask in the title. Suppose $\mathbb{G}$ is a group and $\mathcal{G}$ is a groupoid. Consider their profinite completions $\overline{\mathbb{G}}$ and $\overline{\mathcal{G}}$.

If the completions give the same group, then is it possible to say anything about the relationship between $\mathbb{G}$ and $\mathcal{G}$ ?