Shafa'ah is (intercession) which means that we seek the intercession of the Prophet Muhammad (SAWA) and his Holy Progeny Ahlul Bayt (AS) for our sins to be forgiven by Allah (SWT). The intercession is granted by Allah to those who are allowed to get it from those who are allowed to give it. No intercession but only after permission from Allah. (They will not intercede for anyone except for those whom Allah allows.(Sura 21, Verse 28). Intercession is a Quranic fact and a fact mentioned by the Prophet (SAWA) in many Hadeeths which were narrated by over forty Companions according to نظم المتناثر من الحديث المتواتر Nadhm Al-Mutanaathir Minal Hadeeth Al-Mutawaatir, page 235.
Tawassul is seeking from the best servants of Allah to help us by their Du'a to Allah in our favor. Allah (SWT) ordered us to seek Waseela to Him (O those who believe, be pious and seek the mean (Waseela) to be near to Him) Sura 5, verse 35.
Istighatha is seeking urgent help in distress. We seek urgent help when we are in distress from Allah and from His most humble servants whose Du'a is acceptable by Allah. Direct Istighatha from Allah's sincere servants is mentioned in Quran when a follower of Prophet Musa (Moses) soke urgent help from Musa when he was in danger from his enemy, and Musa immediately came to his rescue and killed his enemy. فاستغاثه الذي من شيعته على الذي من عدوّه فَوَكَزَهُ موسى فقَضى عليه.(Sura 28, Verse 15).
We have the chance to seek urgent help in distress (Istighatha) from Imam Al-Mahdi (AS) who is our present Imam as that follower of Prophet Musa soke urgent help in distress from Prophet Musa (AS).