Yes, she took the money and became angry because you caught her. She was so defensive and guilty that she didn't hear you say you would understand if she needed the money. However, since she quickly replaced it I'd think she didn't take it because she needed it.
Let her cool down, maybe for weeks, before you try to talk with her. My daughter has been so angry with me she wouldn't talk with me and the longest that lasted was a month.
Don't try to figure it out. She is like she is. It's possible that her life is so stressful she has a short fuse. You can't do anything about how she handles stress or even the cause of the stress so just let her work it out for herself.
Painful, I know. But she'll come around in time. I wouldn't bring it up again. She knows she did it and she knows you know. No reason to rehash past issues. Trying to do so will only prolong her anger.