Unboundedness and redundancy are distinct concepts in Linear Programming: unboundedness occurs when the feasible region allows the objective function to increase or decrease indefinitely, resulting in no optimal solution, while redundancy refers to constraints that do not affect the feasible region or the optimal solution, meaning they can be removed without changing the problem's outcome. Essentially, unboundedness signifies an issue with achieving an optimal solution due to infinite possibilities, whereas redundancy indicates unnecessary constraints that do not impact the optimization process.