No they are the same, but a lot of people use the former to mean the latter. England is one of four countries that constitute the United Kingdom [of Great Britain and Northern Ireland] (UK). The other three are Wales, Scotland and Northern Ireland.
The word 'Britain' is a vague term. It can have, inter alia, two meanings. It is sometimes used to refer to the UK. At other times it may refer to the British Islands. That is a political term rather than a geographical one. It refers to the UK and three other jurisdictions. Those are all Crown Dependencies and are not part of the UK or of the EU. They are the Isle of Man, the Bailiwick of Jersey and the Bailiwick of Guernsey and her Dependencies. The latter two are often commonly called the Channel Islands.
Some people may less commonly use Britain to refer to the geographical entity that is the British Islands. That includes the two largest islands of Great Britain and Ireland and many other islands, including the Isle of Man. It does exclude the Channel Islands. Of course, not only is Britain inappropriately used in this context there are some, especially the Irish, who object to the accepted geographical term the British Isles.