我一直分不清楚英语里有一个语法是 I have no choice but 还有I can`t do but

1、but前如果有个动词do,那么but后应该用do sth;
例如：I have nothing to do but do sth
2、but前没有动词do(象这里只是一个名词choice),那么其后用to do sth
例如：I have no choice but to do sth