Question

have no choice but to do sth. have nothing to do but do sth. 分别是什么意思？

Answer 1

have no choice but to do sth. 除了... 别无选择
have no choice but to accpet his invitation.
我除了接受他的邀请没有别的选择。
I have no choice but to believe what you're saying.
我除了相信你说的话别无选择。

have nothing to do but do sth. 除了...什么也没做
例如：I had nothing to do but slept all the time last Sunday.
(我上周日除了睡觉什么也没有做.)

Answer 2

别无他法只能做某事，无事可做只好做某事

Answer 3

1，没有选择的余地，只能做……
2，没事可做，只好做……