The main difference is that someone who are married to a British Citizen can apply for naturalisation as a British Citizen as soon as he/she has Indefinite Leave to Remain (ILR) in the UK. However, those who are only living together as partners can only apply for naturalisation / registration after having ILR for at lease one year.
You need to read my original post carefully -
1) People married to British Citizens - they can apply for naturalisation as soon as they have Indefinite Leave to Remain (ILR) in the UK.
2) A person who is not married to, but living together with a British Citizen - he/she can only apply for naturalisation or registration 12 months after receiving ILR.
Example - Two people, Mrs X and Mr Y receive their ILR today (23 June 2017), Mrs X is married to a British Citizen, therefore she can apply to naturalise as a British Citizen on the 23 June 2017.
Mr Y, on the other hand, is not married to a British Citizen. This means that he can only apply for naturalise or register to become a British Citizen on or after 23 June 2018.
As UK naturalisation and registration fees go up every year, waiting an extra year for naturalisation or registration will cost Mr Y more.