Does saying "Insha'Allah (God willing)" differ from "In Shi'ta (If You will)" when supplicating, and does the ruling change if the intention behind "Insha'Allah" is "My Lord, answer me" without an option?

The phrase "in sha' Allah" (God willing) does not differ from "in shi'ta" (if You will), and both are conditional upon God's will. The prohibition mentioned in the hadith regarding making supplications conditional upon God's will: "None of you should say: 'O Allah, forgive me if You will; O Allah, have mercy on me if You will.' Rather, he should be firm in his request, for there is nothing compelling Him," is a prohibition of discommendation (karahat at-tanzih), not prohibition (tahrim). Some scholars believe that saying "in sha' Allah" after a supplication, if intended for seeking blessings (tabarruk), is not discommended. Others hold that if the supplication is in the form of a statement (khabar), it is not discommended to make it conditional upon God's will, such as saying to a sick person: "May it be a purification, in sha' Allah."