Assalaamu alaikum,
As far as I know there is no difference in schools of thought on this. It is a well established sunnah.
The dhikr after salaah referred to in the question has been reported in a hadeeth reported by Abu Hurayrah from the Messenger of Allaah (peace and blessings of Allaah be upon him): “
Whoever glorifies Allaah (says Subhaan Allaah) thirty-three times immediately after each prayer, and praises Allaah (says Al-hamdu Lillaah) thirty-three times, and magnifies Allaah (says Allaahu akbar) thirty-three times, this makes ninety-nine, then to complete one hundred says Laa ilaaha ill-Allaah wahdahu laa shareeka lahu, lahu’l-mulk wa lahu’l-hamd wa huwa ‘ala kulli shay’in qadeer (There is no god except Allaah Alone, with no partner, His is the power and His is the praise, and He is Able to do all things) – his sins will be forgiven even if they are like the foam of the sea.” (Reported by Muslim, 939).
As regards counting this tasbeeh, the Sunnah is to use the fingers of the right hand. Abu Dawood (may Allaah have mercy on him), said: “ ‘Ubayd-Allaah ibn ‘Umar ibn Maysarah and Muhammad ibn Qudaamah, among others, told us: ‘Aththaam told us from al-A’mash from ‘Ataa’ ibn al-Saa’ib from his father from ‘Abd-Allaah ibn ‘Amr who said: ‘I saw the Messenger of Allaah (peace and blessings of Allaah be upon him) counting the tasbeeh.’ Ibn Qudaamah said: ‘With his right hand.’” (Sunan Abi Dawood, Kitaab al-Salaat, Baab al-Tasbeeh bi’l-hasaa).
It was said in Haashiyat al-Tahtaawi: “It is correct that he (peace and blessings of Allaah be upon him) used to count the tasbeeh on his right hand. It was reported that he said: ‘Count with your finger tips, for they will be asked and they will be made to speak.’ Ibn Hijr said: Counting the tasbeeh with the fingertips is better than using the subhah (prayer-beads or “rosary”).
From:
http://www.islam-qa.com/en/ref/2355
There are also other du'as/ dhikr that can be said after prayer, and are sunnah to say. I will try and find some with transliterations.
For now:
Astaghfirullah [meaning: I seek Allah's forgiveness] (3 times),
Allaahumma antassalaam wa minkassalaam tabaarakta yaa dhal jalaali wal ikraam
Meaning: O Allaah, You are Peace and from You is all peace, blessed are You, O Possessor of majesty and honour. (Once)
These two to be recited right after the last salaam of prayer, i.e. recite these adhkaar (plural of dhikr) first, then any others.
Assalaamu alaikum