予算 and 会計: a planned budget and the actual bill
Distinguish a purchase budget from restaurant checkout, reading cases where the amount spent differs from the planned amount.
A spending plan set in advance
予算, read よさん, means a plan for income and expenditure or the amount available to spend. 贈り物の予算は三千円です。 says that the gift budget is three thousand yen.
予算内で選びたいです。 says that the speaker wants to choose within the budget. 予算 does not report a payment already made.
Calculating money or paying at a shop
会計, read かいけい, refers to accounting for money or paying a bill at a shop. 食事が終わったので、会計をお願いしました。 says that the bill was requested after the meal ended.
会計は入口のレジでお願いします。 asks customers to pay at the register near the entrance. It does not ask them to submit a planned meal budget.
The planned amount and the actual amount
予算は三千円でしたが、会計は二千五百円でした。 says that the budget was three thousand yen but the bill was two thousand five hundred yen. The amounts have different roles.
会計を済ませてから店を出ました。 says that the bill was settled before leaving the shop. Separate deciding a budget from completing actual checkout.
Does 食事のあとで会計をお願いします。 request help preparing a meal budget?
Show the answer and why
No. In this restaurant context, it requests calculation or settlement of the meal bill.