A cutting tool (in Japanese, a "bite") is the tool that cuts the material on a lathe.
An insert is the replaceable cutting tip mounted at the end of that tool.
When the edge wears, only the insert is replaced.
A Closer Look
Brazed tools, which were resharpened as a whole, were once the norm; today, the "indexable" system — replacing only the insert when it wears — is used almost universally.
This eliminates resharpening and allows machining to continue at a consistent quality.
Inserts come in many varieties of material (HSS, carbide, and more), coating, shape, and nose radius, and are chosen to suit the material and the operation.
Choosing the right insert governs both machining quality and tool life.