Lord Shiva is popularly known as Shankara or Samkara. Samkara means doer of good deeds or who is the same or stable in all deeds. The word Shankar is made up of two words, namely "shanka" and "hara". Shanka means doubt and hara means dispeller or destroyer. It also means lord.

Lord Shiva is popularly known as Shankara or Samkara. Samkara means doer of good deeds or who is the same or stable in all deeds. The word Shankar is made up of two words, namely "shanka" and "hara". Shanka means doubt and hara means dispeller or destroyer. It also means lord. The word "Shankara" thus means He who dispels or destroys doubts. By dispelling our doubts and establishing faith, He destroys all our bondage. Shankara or Sankara also inply sankata + hara, that is he who destroys or ends all difficulties. Sincere prayers to Shankara are very effective. The Lord is easily pleased with pure devotion and responds immediately. Shiva is known for his boon giving nature. 
In Shiva Purana its stated that Shiva created Shankara. From Shankara left hand side came Vishnu, From right hand side Mahadev and from Vishnu belly button came Brahma.
As per Linga Purana ,That linga was surrounded by thousands of flames and hot like fire of death. Without any beginning, middle and end, that was free from decay and growth. This endless form of bright light is known as Shiva.
As per Vishnu Purana and Gita , of all the Rudras he is Shankara! But Shankara, Rudra, Mahadev mean the God who dwells in the Kailash. And Shiva means His absolute formless mode of bright light.
Acc to Kurma Purana, Shankara is a Rudra. Shiva and Shankara both imply the same deity, Shiva means his formless pure bright light form, meditated upon by Yogis and Shankara means his commonly known Kailash dwelling ascetic form, worshiped by devotees.
So from above references, it's clear that there is a subtle difference, or rather no difference between Shiva & Shankara, both names are of the supreme Brahman!
Jai Shiva Shambhu ~ Jai Shiva Shankara!