They will need a Eurail pass which is better as they do not have the 2-day restriction in the country of residence

You must check that your parents' visa allows travelling in the Schengen area as UK not is a part of Schengen. 

As far as I can see your parents need a Schengen visa in addition to the UK visa if they want to travel outside of the UK. 

https://www.schengenvisainfo.com/who-needs-schengen-visa/

Hopefully your parents applied for both visas at the same time. 

https://btwvisas.com/schengen-visa/uk-schengen-visa

Thank you @AnnaB, yes, sorry I forgot to mention they did have Schengen visa for the Europe trips, it is short stay visa, for multiple entry with no more than 28 days for each time. 
My question is if they can purchase interrail tickets instead of Eurail ticket? 
Thanks! 

Thank you @thibcabe, what is “2-day restriction in the country of residence” for interrail? Thanks! 

The outbound/inbound rule for Interrail passes says that you are only allowed to travel in your country of residence on a maximum of 2 travel days. With Eurail there are no such restrictions and your parents cn travel on more than 2 travel days in the UK. Thus a Eurail pass gives you more possibilities to travel in the UK.

If you have a non European passport you can also   travel with a Eurail pass. 

Thank you @AnnaB , we don’t plan to use the train in UK, we will fly to Europe and then will take the trains in Europe. I don’t plan to buy Eurail pass.
My question is interrail is eligible for temporary residence in UK or Europe countries. Will my parents with short stay visa in UK consider as temporary residence and eligible for purchase the interrail pass? 
Thanks a lot! 

(We will drive in UK)

No they’ll have to buy to a Eurail Pass. It isn’t more expensive than an Interrail Pass. It is exactly the same pass but for residents outside Europe. You, as you live in the UK, will buy an Interrail Pass if you’d like one

Thank you @thibcabe, we will mainly use the train in Switzerland in 2-3 days, I found SBB “day saver” tickets is cheaper and more flexible than Eurrail pass or Interrail one country pass. I will get day saver tickets instead. Thanks a lot! 

(Saver Day Passes )

Yes they're valid on all Swiss trains, buses, boats, trams and some cable cars. Great value at 52 CHF per day (full-fare) when bought in advance.

On the other hand it does not give any discount for mountain railways such as Jungfraujoch, Gornergrat or Titlis. If you'd like to go to any of these buy a half-fare card (120 CHF) + half-fare saver day passes or half-fare tickets for short journeys.

Jungfraujoch : 110 CHF instead of 220 CHF

Gormergrat : 64 CHF instead of 128 CHF

Titlis : 49 CHF instead of 98 CHF