for the holiday on the holiday during the holiday 的区别

1 They go to London for their holiday-------目的是度假.
2 They go to London on holiday (应该没有the) -----目的是度假.
3 They go to London to see their daughter during the holiday ------强调在假期裏面.
4 on one's holidays == having a holiday------ 强调在度假.