English and British refer to citizens from different places such as other examples like African, American, Chinese, Russian, etc. Many people actually think these two different citizenships are the same; meanwhile, they are really different. To understand the difference, we will have to explain the geographical location of the environment these citizens come from. Now, understand that someone from England is referred to as English, while someone from any of the countries in the Britain colony (British Isles) is called a British.
Back to the geographical explanation, England only happens to be a country in the British Isles. Meanwhile, the British Isles include different countries such as England, Scotland, Wales, Ireland, and a few others. Hence, English is also a British, but a British is not necessarily English. In addition, the population of the British is far more than the population of English. I believe you now understand the difference between English and British.