What are the key differences between a deterministic and non-deterministic Turing machine in terms of their computational capabilities and problem-solving approaches?

A deterministic Turing machine follows a single path of computation based on its input, while a non-deterministic Turing machine can explore multiple paths simultaneously. This allows non-deterministic machines to potentially solve problems faster, but their solutions may not always be correct. Deterministic machines are more reliable but may take longer to solve certain problems.