Note the BritRailpasses are a own offer of the British Railcompanies and is not realted to Eurail. Reservations within the UK are free except for the Nighttrains. 

I recommend to compare the different offers and find out wich pass is the best for you 

Interrail/Eurail globalpass or OneCountryPass Great Britain 
or 
the BritRailpasses.

In the post How to get Reservations you can find many helpfull information.

Different prices from retailers has been a thing for a long time with Britrail, no idea why. Both those are genuine retailers so whichever is cheaper.

The full Britrail pass has very similar validity to Interrail one country Britain pass, that is they are both valid on nearly all rail services, Heathrow Express being an exception that is valid with Britrail bit not Interrail.

The other main difference is ease of use, with Interrail you either have to fill out every journey on paper travel diary or enter each journey into the interrail app, activate and create passes for each day. With Britrail just download the PDF and show it on your phone or print it out (or both, use phone but keep printout as backup).

Reservations are not mandatory except for night sleeper trains. They are free from British station ticket offices or online by making an account on www.gwr.com , ACP Rail( and possibly other agencies selling passes) charge a large fee for reservations, this is a very bad deal, DO NOT PAY FOR BRITISH RAILWAY RESERVATIONS from these sites.

NO-at least in the past 1-country passes did NOT have the need to write down all trips-in paper version. But Ive never used the mobile so cannot comment-it may be that all the enormous colourful variety of all those GB-´private´ concessionaires who won their right to run some trains now also want this in fair share of the takings

Thank you for your response! It´s very helpful! I have the last question, I want to buy it from International Rail but I didnt find the mobile option, and cause I don't live in the UK I don't have an address where they can deliver the pass. Do you know if I can download it regardless that I purchased for the print version?

If they are not offering the mobile version then no you can not print out the paper pass. This is printed on official paper and comes in a cover both of which make up the ticket.

Do not buy paper pass if you are not certain you can receive it in good time.

I have not used them but I am sure they deliver to most countries, in fact the one country that they are likely not to deliver to is UK as the passes are not available to UK residents.