ILR is Indefinite Leave to Remain, but can also known as "Residency". However Citizenship, or "Naturalisation" is when the applicant aquires a British Passport, so becomes British.
I know of people who have had ILR for years and wont bother with Naturalisation. Its not compulsory to take Naturalisation, as ILR is Indefinite, but it is a good idea, saves hassle when travelling. A British Passport gets you lots of place. For example, if you are a Filipino Passport holder with a UK ILR stamp, you would still be subject to UK Immigration everytime you re-enter the country, but with a UK passport this would not be the case.