Actually this is a very keen and advanced question! ～から出る means going out of certain range physically to the outside, with or without a will. Also it doesn't matter if you go somewhere else or not. For example, 「火事だ！玄関からは出られない！どうしよう？」 「あそこの窓から出ましょう！」 'Fire! We can't g out from the entrance. What should we do?' 'Let's evacuate from the window over there.' から works better here because they are discussing which exit to use to get out from the place. 「窓から庭に出れば安全でしょう。」 'It should be safe if we get out from the window to the yard ' Only から works for this example because of 庭に. If ～から and ～に share a verb, 出る, you should use から. 目から涙が出る。'Tears run out from eyes.' (You can't use を in this case because 涙 doesn't have a will to leave. Same for other "things" that have no hearts.) ～を出る means leaving a place physically or not physically with a will to leave, and implies going somewhere else. 彼は東京大学を出て、銀行に就職した。 'He graduated from Tokyo university and got a job in a bank.' (You can't use から here because this 出る means 'to graduate', not walking away from the place. ) 彼女は就職して両親の家を出た。 'She got a job and left the parents' home. ' を is better for this sentence. She left the parents' home physically and mentally to be independent. In a room... 「トイレはどこですか？」 「あの緑のドアを出て、右に曲がってください。」 'Where is the restroom?' 'Leave from that green door, then turn right.' を is better here because leaving the room is just a part of entire trip to the restroom. クラスが終わるまで、教室から出ないでください。 クラスが終わるまで、教室を出ないでください。 'Don't leave the classroom until dismissed.' Both works. The students have their will to go out/leave, and they may or may not go somewhere then.

~kara mean action one to another Like A kara B action change to a from b Your case "~kara deru" ~ leave some place to other place " ~ Wo " explan to object or place Your case ~ Wo deru mean leave somewhere. Deru mean action of out going.therefere meaning is very close.

i am a beginner in Japanese and i am not sure about the answer, but i think that から出るmeans to take out from like かばんから出ます。to take it out from bag. but を出る means "to leave somewhere" like うちを出ます。