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Key terms:
Re-entry permit is used to enter on a previously obtained, valid permission to stay stamp. Obtained at the local immigration office and some of the international airports (land borders usually do not issue them). Cost is 1000 baht for single re-entry and 3800 for multiple re-entry permit. The permit is tied to the permission to stay in which you intend to re-enter. You must obtain this before exiting the country.
Extension of stay is used to extend or increase your existing permission to stay. Obtained at the local immigration office for 1900 baht + 1 passport photo. Most tourists qualify for 30 days, and some special categories (like visiting Thai family) can obtain 60 days or even 365 day extension of stay)
I am from Italy and as such I have a 30 days exemption visa to enter Thailand. This will be valid until the 21st of February. Tomorrow 16th of February I will leave Thailand for Malaysia, but I plan to go back to Thailand on exactly the 21st and stay till the 28th of February.
Ok. if you want to reuse an existing permission to stay, you must first obtain a re-entry permit from a local immigration office (not usually a border immigration office) or some of the international airports have re-entry permit issuing service. This does not extend your existing permission time.
You could theoretically extend your stay for 30 days at local immigration office first (1900 baht) and then immediately apply for a single re-entry permit (1000 baht).
Of course another [simpler, cheaper] option is to just enter again on a visa exempt and get another 30 day stamp. This should be fine if you don't have a history of entering the country repeatedly on visa exempt based entries over the previous 2 years.