Shestheone and Greymary both petitions are separate protests about the same subject.
38 Degrees is an independent British not for profit organisation that campaigns on a wide range of issues. It aims to give a voice to ordinary UK citizens, by providing easy ways for them to take action on the issues they care about, e.g. climate change, human rights and poverty. The organisation was started in 2009 during the last Labour government as the MPs' expenses scandal grew, demanding voters should be given more powers to sack MPs. One of the founders is Gordon Roddick, co-founder of The Body Shop and husband of Anita Roddick.
The other petition is on the government's e-petition site. In theory, at 10,000 signatures you get a response from the government, and at 100,000 signatures your petition will be considered for a debate in Parliament. In reality, many petitions exceed this threshold and lead to no debate. They are passed to a backbench committee for consideration and response and that's the end of the campaign.
Digital campaign platforms such as change.org and 38 Degrees are far more successful than the government's e-petition site. A petition is often the start of a long campaign for change.
A good example was the fight to stop the government selling off the national forests. Over half a million 38 Degree members signed the petition against this policy. Then 38 Degrees brought together its members with local and national organisations like the Woodland Trust, the National Trust, the British Horse Society and Ramblers.
Over 100,000 38 Degrees members emailed or called their MPs urging them to stop the forest sell off.. Hundreds of 38 Degrees members donated to fund a YouGov poll which found that 84% of the public wanted the forests kept in public hands. Thousands of 38 Degrees members chipped in nearly £60,000 to pay for ads in national newspapers to highlight that 84% of the British public opposed the forest sale. The campaign lasted more than 2 years and led to the government revoking the policy. Incidentally, John Major's government considered adopting this policy and decided against it because of the potential public backlash.
Hope this helps.