Implied (tangency or curvature) is typically used for maintaining continuity across a centerline or mirror plane. For example if you’re building to a curve on the center line and just have it set to free or fixed, it will only try to get positional continuity to that point, which may or may not have tangency when you mirror it across the centerline. By setting implied tangency/curvature it tries to achieve tangency to that mirrored surface across the edge.
Rebuild means the tool will go in and rebuild the edge that you are specifying. You generally don’t want to rebuild if you are building to a clean edge (natural surface boundary or a curve) but do want to rebuild if you’re building to a complex surface or trimmed edge. This will reduce your # of spans and help improve the isoparm distribution while matinaining continuity.
Alternatively you can use explicit control to specify the exact surface parameters you want but this may not achieve continuity without further tweaks.