当日 and 即日: an event date and same-day processing
Compare collection on a performance date with same-day issuing after an application, separating timing from instant or free service.
The date of the identified event
当日, read とうじつ, refers to the day of an identified event. 公演当日は入口で券を受け取ります。 says that tickets are collected at the entrance on the performance date.
旅行当日は早く起きました。 says that the person got up early on the day of the trip. It does not identify that date as today.
Processing on the day of the request
即日（そくじつ）は申し込んだその日に処理することを表せます。 explains that 即日 can describe processing on the same day as the application.
この証明書は即日発行できます。 says that this certificate can be issued the same day. It does not promise issuing at the instant of application or free service.
Identifying the reference day
公演当日に申し込むと、即日受け取れます。 says that an application on the performance date allows collection that same day. In this example, the two reference dates are connected.
即日対応はできません。 says that same-day handling is unavailable. It does not rule out handling the request on a later day.
Does この証明書は即日発行できます。 establish that issuing is free?
Show the answer and why
No. It supplies same-day availability. Fees and the exact processing time require separate information.