Out of the five [*schools*] mentioned by VyAsar, the remaining two apart from vEdA, sAnkhyA and yOgA are pAncharAthram and pAshupatham.
In pAncharAthram, Vishnu alone is identified as the God; while in pAshupatham, only SivA is seen as the God. These schools denigrate other deities and hold only specific deities as the supreme Godhead.
As though VyasAchAryA was of the opinion that these two schools are non-vEdic in nature, He has mentioned the vEdha matham separetly as 'vEdhA:', and grouped these two as sampradhAyams, differening from vEdAs, by making a separate mention as 'pAncharAthram, pAshupatham'. Sankhyam is a mere philosophical speculation (thathva-vAdham) only. In that, there is neither karmA; nor bhakti; nor any means to the experience of gyAna. Though yOgA is a school held in very high esteem, there is no scope for vaidhIka upAsanA and karma in it. Even with regards to gyAna, there is not so much clear expositon about the 'paramAthma thathvam', as it is in upanishads.
As these four schools are 'apUrnam' in one way or the other, He has distinguished them from the complete (pUrna) vEdA [*matham*], which possesses all the [*postive*] aspects of these schools, by naming them separately.
VyAsar is a Maharshi. Absolute gyAni. If His opinion was like this, there was another - who was a gandharvA, took birth as a human due to a curse of ambAl, became a great Siva bhakthA, sung in praise
of Ishvara, obtained the very Ishvara as a result and finally became a permanent resident of KailAsam (nithya-kailAsa-vAsi). His name is Pushpa dhanthar. The sthOthra that he composed is known by the name -
'Siva mahimna sthOthram'. It means that 'the sthOthra that talks about the greatness of Siva'.
Through out North India, starting from those regions lying to the north of Pune, there would be no bhakthA(s) who would not know [*this*] Siva mahimna sthOthram. (In our region [*Tamil Nadu*], neither ThiruppAvai  nor ThiruvembAvai  nor Thiru-murugu-Atrup-padai  nor VinAyagar agaval , became so popular even after my repeated persuations and getting them printed as books and distributing them).
As VyAsar had mentioned [*in His verse*], even in this sthOthrA, there is a reference to various schools. This looks as though Pushpa dhanthar has composed his slOka keeping the verse from MahAbhArathA in mind:
 This a most celebrated devotional work by AndAl on Sriman NArAyanA. More details on this work can be obtained from the VishishtAdvaita home page.
 This is a devotional hymn sung by the famous saivaite saint MAnikka vAsagar, in praise of Lord Siva in a nayaki bhAvam. Both these works together used to be sung during the month of mArghazhi [Dec 15 - Jan 14].
 Thiru-murugu-Atrup-padai is a work on Lord SubhrahmanyA by the Tamil poet NakkIrar, poet laurate of Pandya king, ruling the south Indian city of Madurai during 'Sangam' period.
 This is a composition, full of yOga sAdhana details, sung in praise of Lord GanEshA by His poetess devotee 'Ou-vaI-yAr'. The speciality of this work is the lucid elaboration of Her spiritual progress, step-by-step, in the 'agaval' metre.