With a separate terminal, staff normally enter the payment amount on the terminal and record the sale in the till. An integrated setup can pass the amount from the till to the payment device, but the exact behaviour depends on the supported till, terminal and payment provider.
Before choosing, ask for a demonstration of a sale, refund, split bill and end-of-day reconciliation using your intended setup. Check whether stock, kitchen printing, table management and staff permissions are included in the software price or require additional subscriptions.
Ask who supports each part of the system, who you call if a payment succeeds but the till does not update, and what happens during a connection failure. Do not assume a terminal works with a till simply because both are described as smart.
Share the till name, software version if known, business type and the workflow you are trying to improve. Which integration has saved you the most manual work?