What's the difference between backstair and backstairs?

Backstair

Definition:

• (a.) Private; indirect; secret; intriguing; -- as if finding access by the back stairs.

Example Sentences:

• (1) The backstairs briefings against him were totally unacceptable.
• (2) But they are part of Labour's backstairs compromise which saw around 700 hereditary peers expelled from the upper house in 1999.
• (3) Mummy was like, so just do the same with Kerslake, it is an excellent backstairs name, I'm like, we did – how do you think we lost Helen Ghosh and David Bell – but there still about 10 million Kerslakes left?

Backstairs

Definition:

• (a.) Alt. of Backstair

Example Sentences:

• (1) The backstairs briefings against him were totally unacceptable.
• (2) But they are part of Labour's backstairs compromise which saw around 700 hereditary peers expelled from the upper house in 1999.
• (3) Mummy was like, so just do the same with Kerslake, it is an excellent backstairs name, I'm like, we did – how do you think we lost Helen Ghosh and David Bell – but there still about 10 million Kerslakes left?