Following are the various applications which can be submitted to the Home Office on the basis of a person's long residence in the UK:

Indefinite Leave To Remain (ILR) On The Basis Of 10 Years Continuous Lawful Residence

A person who has lived in the UK continuously and lawfully in the UK for 10 years can apply for Indefinite Leave to Remain (ILR) on the basis of his 10 years long residence. Such application is made by completing application form SET (LR). We can provide Same Day Visa Service for the ILR applications on the basis of 10 Years long residence

Extension Of Stay On The Basis Of 10 Years Long Residence

If you do not qualify for ILR on the basis of 10 years long residence e.g. becuase you could not pass the Life in the UK test or you have a criminal conviction which will become a reason for refusal of your ILR application, you can apply for extension of stay on the basis of 10 years long residence. An application for extension of stay on the basis of 10 years long residence is submitted using application form FLR (LR). 

Limited Leave To Remain On The Basis Of 20 Years Continuous Residence In The UK

A person who has lived in the UK for 20 years continuously can apply for limited leave to remain on the basis of 20 years long residence. Application for stay on the basis of 20 years long residence is made using application form FLR (FP) and the successful applicant will be granted leave to remain for 30 months under the 10 years route to settlement.