Outside vs inside
An outside corner turns around a projecting corner — the standard corners of a rectangular house. An inside corner folds into a recess, such as where a wing meets the main body or an L-shaped plan turns back on itself.
The practical difference is water volume. At an outside corner the two runs generally carry water away from the joint. At an inside corner both runs feed toward it, so the joint sees far more flow — which is why inside corners fail more often and why we look at them first.
How they are made
Either as a strip miter, folded from the gutter itself on site, or as a box miter using a prefabricated corner. A strip miter has one seam and a cleaner look; a box miter has two seams but is more forgiving of an imperfect angle. Neither is wrong — what matters is that the joint is sealed from the inside, so water pressure pushes the seal closed.
Why they leak
Sealant fatigue, essentially always. Kansas City runs a hundred-degree annual temperature swing, and aluminum moves with it. Over a decade or two the sealant in the joint goes hard, shrinks back from the metal, and opens a hairline gap. From the ground the symptom is water running down the outside of the corner during rain, and a stain on the fascia below that never quite dries.
What a proper repair looks like
Not a fresh bead over the old one — new sealant does not bond to degraded sealant, which is why that patch comes back. The joint gets opened, both faces cleaned to bare metal, and re-sealed from the inside. Done that way a corner repair is a repair, not an annual appointment.