Grinding
A cutting wheel reduces the stump to chips, usually to a depth agreed in the estimate. Less disruption to the surrounding yard, faster in most cases.
Removal
More of the stump and root mass is taken out. It moves more soil, needs more room, and is often chosen before construction or replanting.
Which one fits your plan?
If you want lawn back, grinding often works. If you plan a patio, fence line, or new tree in the same spot, say so, since that changes what the contractor recommends.
What neither one promises
Neither approach guarantees that every root is gone or that nothing will regrow, settle, or attract pests later.
Services are performed by independent local contractors. Scope, access, scheduling, and pricing are confirmed by the contractor.