The Sharia', also transliterated from the Arabic xxxxx as Shar'ia, is the system of jurisprudence and codes from proper conduct drawn from sources including the Qu'ran, traditional (primarily Arab) traditions, the Sunna, and the Hadiths. It draws Arab Bedouin law, commercial law from Mecca, agrarian law from Madina, law from the conquered countries, Roman law and Jewish law.
Sharia is not strictly Islamic law, which depends strictly on the Qu'ran. Only a small part is irrefutably based upon the core Islamic text, the Koran. Correct designations would be "Muslim Law", "Islam-inspired", "Islam-derived," or even "the law system of Muslims." Sharia is always referred to as "based upon the Koran", hence it is the "will of God."
Islamist refers to government run by the rules of Sharia, but, with the caveat that Islamists do not separate between religion and state, Islamist principles are as much political as theologicsl.