Hard Limit of Computability
The hard limit of computability is reached when something is uncomputable, i.e. there can be no algorithm that provides a solution to an uncomputable problem. Undecidable problems reach the hard limit of computability.
Undecidable problems are problems for which it is impossible for there to be an algorithm that always gives a correct solution to a decision problem.
Soft Limit of Computability
The soft limit of computability is reached when a problem can be solved, but requires an impractical number of resources (space or time) to be solved. Intractable problems reach the soft limit of computability.
Intractable problems are problems that cannot be solved in polynomial time, and so grow rapidly compared to the input size. This makes them impractical to solve for large inputs.