順番 and 順序: turns and sequences
Distinguish turns in a queue from the sequence of a process, including areas of overlap.
Saying whose turn it is
順番 is read じゅんばん and refers to the order in which people or actions take their turn. 「自分の順番を待ってください」 asks someone to wait for their turn.
「順番に名前を呼びます」 says that names will be called in order. Whether the order is based on arrival or names must be stated separately.
The arrangement of a process
順序 is read じゅんじょ and refers to the sequence of steps or elements. 「作業の順序を確認しました」 means that the speaker checked the sequence of tasks.
「順序を逆にすると、うまくいきません」 says that reversing the order will prevent things from going well. It is a condition, not a statement that someone already reversed it and failed.
Recognizing overlap
Both 「説明する順番」 and 「説明する順序」 can refer to the order of explanation. 順番 suggests turns and 順序 an arrangement, but not every context permits only one correct choice.
At a service desk, 「私の順番ですか」 naturally asks whether it is your turn. Identify whether the issue is someone's turn or the structure of a process rather than simply swapping words.
Does 「順番を変えてください」 necessarily ask someone to change the method of doing the work?
Show the answer and why
No. It asks for a change in the order of people or actions, not necessarily in how an action is performed. Context identifies what is being reordered.