後日 and 別の日: a later day and a different day
Compare later notification with a photograph taken on another date, distinguishing a change of date from a specified later time.
A day after the reference event
後日, read ごじつ, identifies a later day. 詳細は後日お知らせします。 says that details will be provided later.
後日、改めて訪問しました。 reports that another visit was made on a later day. 後日 does not by itself put the whole sentence in the future.
A date that differs
別の日, read べつのひ, means another day. この写真は別の日に撮りました。 says that this photograph was taken on a different day.
別の日 does not by itself establish whether that date was earlier or later. A description using 別の日に撮った may specify only a difference of date.
Separating difference from chronological order
その日は都合が悪いので、別の日にしましょう。 suggests choosing another day because the stated day is inconvenient. A replacement date still needs to be selected.
当日の写真と、後日撮った写真を比べました。 says that photographs from the event date were compared with ones taken later. Here 後日 specifies chronological order.
Must the photograph have been taken after the event in この写真は別の日に撮りました。?
Show the answer and why
No. The sentence only says that the date was different. It does not establish whether it preceded or followed the event.