Does this characterization apply to solutions $\gamma[ \, t \, ]$ of $$ \nabla_{\dot \gamma} \! \left[ \, \frac{\dot \gamma}{\|\dot \gamma\|} \, \right] = 0 \tag{1} $$ ?
Wikipedia continues:
"A geodesic on a smooth manifold $M$ with an affine connection $\nabla$ is defined as a curve $\gamma[ \, t \, ]$ such that parallel transport along the curve preserves the tangent vector to the curve, so"
$$ \nabla_{\dot \gamma}[ \, \dot \gamma \, ] = 0 \tag{2}$$
Is there additional terminology available for distinguishing between solutions of eq. (1) and solutions of eq. (2) ?