A logical failure typically refers to corrupt or lost data on a disk with no physical problems. This can be caused by an operating system failure, a virus infection, unintentionally formatting a drive, accidental deletion of files, or (rarely) static damage. A physical failure is when the device itself is physically damaged and needs repair or replaced components.
Damaged head disk assemblies, spindle motors, failed circuit boards, corrupted firmware, and damaged platters, are a few examples of physical damage. When a physical failure occurs, typically the hard drive makes strange noises (e.g., clicking, beeping, grinding), or will not be recognized by BIOS. If there are any noises or sounds, or you suspect a physical failure, stop using the drive right away and contact a specialized data recovery company to minimize the risk of a critical data loss.