The difference between Mujassim and Mushabiha is that the Mujassima attribute body to Allah but don't liken him to his creation while the Mushabiha attribute body parts to Allah and liken him to the creation.
You know there is a difference between, he was accused of doing something and he did something. Misguided groups always used to wrongly accuse Ahlus Sunnah and its Ulema of Tashbih from the Jahmiyyah and Mu'tizilah of the past to their modern-day descendants in the form of Ash'ariyah and Maturidiyaah.
Sheikhul Islam was imprisoned for other things that had nothing to do with blasphemy. The only time he was questioned for his Aqqeeda was in the year 705 Hijri and the judges of all four Madhabs agreed that his creed was sound.
قال ابن رجب الحنبلي: ثُمَّ امْتُحِنَ سَنَةَ خَمْس وَسَبْعُمَانَةَ بِالسُّؤَالِ عَنْ مُعْتَقَدِهِ بِأَمْر السُّلْطَانِ، فَجَمَعَ نَائِبُهُ القُضَاةَ والعُلَمَاءَ بالقَصْرِ ، وَأَحْضِرَ الشَّيْخُ، وَسَأَلَهُ عَنْ ذَلِكَ، فَبَعَثَ الشَّيْخُ مَنْ أَحْضَرَ مِنْ دَارِهِ العَقِيْدَةَ الوَاسِطِيَّةَ فَقَرَءُوْهَا فِي ثَلَاثِ مَجَالِسَ، وَحَافَقُوْهُ، وَبَحَثُوا مَعَهُ، وَوَقَعَ الاتِّفَاقُ بَعْدَ ذَلِكَ عَلَى أَنَّ هَذِهِ عَقيدَةٌ، سُنِّيَّةٌ ، سَلَفيَّةٌ