How it works
Formatting creates the structures a filesystem uses to organise files within a storage volume. Choosing NTFS, exFAT or another supported filesystem changes which devices and features can use that volume. Creating partitions, formatting a volume and assigning a drive letter are related but different operations. None should be used casually to make an unfamiliar disk appear in a file browser when it may contain important data.
A quick format replaces filesystem information without comprehensively overwriting the volume. It is therefore not a secure disposal method. It can also make existing files harder to recover. A disk asking to be formatted may have an unsupported filesystem, damaged metadata or another access problem; the message alone does not establish that the disk is empty. Likewise, a successful format does not prove that deteriorating hardware is reliable.
Practical checks
Identify the target by capacity and model, not only by a drive letter that can change. Verify a backup before confirming a destructive operation and disconnect unrelated removable drives to reduce confusion. Choose the filesystem required by the intended computers or appliances. If the aim is recovery, stop writing to the affected storage and investigate access first. For disposal, use the manufacturer's appropriate sanitisation procedure rather than assuming ordinary formatting removes every recoverable trace.