When you say something will be done today, it means you intend for it to be completed by the end of the day.
In the case of things that don't take the entire day to actually do, you are implying you have the task on some sort of checklist or it is otherwise among your plans to complete for that day.
Today, I'm going to the store.
By the end of the day, you want to have gone to the store, and have that task completed. This is something you are or have been planning to do.
How can I help you today?
You are implying here that you want to have successfully helped the customer by the end of the day, even though the visit may not take the entire day.
The notion of a day when talking about "today" can be flexible according to the person speaking. A 2nd shift (3pm-11pm) or 3rd shift (11pm-6am) worker may still say he/she has to get things done "today", although "tonight" would work similarly.