What's the difference between nadiao and qudiao? 我想知道拿掉和去掉的区别。

The other day I had written "不能出去钓鱼" (bu neng chuqu diao yu, can not go fishing) to a friend and she corrected me and said "把出字去掉" (ba chu zi qudiao, remove the 出), i.e. 不能去钓鱼 (bu neng qu diao yu).

I think I have heard Connie say 拿掉 (na diao) in a lesson and at that time I thought 拿掉 meant "remove" too. Is there a difference between 拿掉 and 去掉? Can both of them be used to mean remove, get rid of, discard and so on?