This is not necessarily an easy question to answer because of the wide range of meanings 'plan' has in English, but I will try in any case!
For me, 予定 is something that you (strongly) intend to do, and likely have made arrangements for too. Looking at the kanji might help here: 予 imparts the meaning of 'beforehand', and 定 imparts the meaning of 'determine' or 'fix'. So this is something that is "determined beforehand". So, it can sometimes also be translated as 'schedule' or 'arrangements'.
On the other hand, 計画 is more of a plan in the sense of a design, or a strategy. In my mind, 計画 typically involves some thought process. I think it can be distinguished from 予定, in that 計画 has an underlying goal or aim, and so often lays out a set of actions to achieve something.
Examples of 予定：
I have no plans (I'll be free) this evening.
Construction work has been scheduled. (i.e. a date has been set)
Example of 計画：
A sales plan
The gang was planning a robbery.
Let's discuss that plan.
Looking at your examples:
休暇の予定がありますか。has for me a meaning of
What do you intend to do on your holidays; have you made arrangements yet?
On the other hand:
has for me a meaning of
I haven't yet started to plan (design) a trip.