Difference between UK Residency and Citizenship?

If you have a British passport you already have citizenship. You cannot be issued a passport unless you are a citizen.

I assume one of your parents is British born and that is why you are a citizen by descent. Because British citizenship can only pass down one generation outside the UK, anyone born outside the UK to a British born parent is a citizen by descent. If you were born inside the UK you would be a citizen otherwise than by descent as would someone who became a citizen through naturalisation. The only difference between 'by descent' and 'otherwise than by descent' is that 'by descent' citizens can only pass down citizenship to their children if their children are born in the UK. All British citizens have right of abode in the UK.

Residency is the term used for actually living in the UK. For example, to be eligible for home fees at a UK education establishment you would have to be resident in the UK (or another EEA country) for at least three years prior to the start date of your course, otherwise you must pay international fees. This applies to any nationality including Britons. Likewise, to be eligible for any welfare benefits you have to establish ordinary residence which is usually between three to six months.

Another use of the term residency is used in the Hague Convention on Child Abduction where countries agree that the courts of the child's habitual country of residence, regardless of its nationality, take precedence in deciding the child's future. So if a child is abducted from Australia to the UK and the child is English but the child's habitual country of residence is Australia, the UK courts will co-operate with Australia in ensuring the child is returned.

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The single most important criteria when applying for a passport is that you are a citizen of the country - a British passport has been issued to you because you are a British citizen, if you weren't they would have taken your fee & written you a polite letter telling you didn't qualify for one, you don't need to apply for citizenship

A person can have residency & not be a citizen of a country - residency is what it says on the tin, a person is a resident of a country, to achieve residency you move to the UK, for most purposes if you're a citizen once you've been resident for six months or more you're considered resident permanently, you don't need to apply for residency in the UK if you're a British citizen or a citizen of an EU member state

British citizenship allows you to settle in the UK, or any other EU member state, and do what you wish, work, study etc (some of the EU member states will require you to register with their authorities if you intend to settle there)

The benefits that are gained by being a citizen and resident vary - for instance if you were to up & move now to the UK you would have no right to claim benefits, housing, free healthcare because you have never been legally resident and some services are dependent on whether or not you've contributed to the system by paying tax & national insurance. If you wanted to attend University in the UK right now as you are not resident & won't fulfil the residency criteria you would be charged international fees - to qualify for home fees & student loans you need to be resident in the UK for 3 years before the first day of the start of your course. If you want to study you can support yourself with part-time work & as a citizen there is no impediment to the number of hours you work

If you have a British passport you are a citizen, unless you want to know how someone else would gain citizenship there isn't much I can add. A person seeking to naturalise as a British citizen needs to legally resident in the UK for 5 years & can only have left the country for a fixed number days in that time - if you're planning on moving to the UK with a partner who doesn't have either British citizenship or citizenship of another EU member state then you need to edit your question & ask how to do that