When people use 終了 it carries more of the meaning that something is over. It's not necessarily completely finished, because it may be stuck at a dead end due to problems or time constraints or any other number of reasons. 完了 on the other hand means to be completely finished. If you look at the kanji, 完 means perfect, so you can think of this as a "perfect" finish. Everything that they set out to do has been completed.

People can say 完了, if they are sure that they have finished doing everything they planned. But a project can come to the state 終了 due to; change of strategy, budget, political or many other reasons.

終了 means finished. 完了 means accomplished.

終了=end 完了=finish