I don't think there is any problem if both the list are simultaneously correct. :)
For the time being I can give you the relevant verses from the Mudgala Purana. According to this Purana Lord Ganesha took 8 incarnations to kill 8 specific Daityas.
Quoting from the article "Ganesha Mahima":
Mudgala Purana details various manifestations of Ganesha as of killing
Vakratundaavataarascha dehaanaam Brahma thaarakah,
cha simhavaahanagah smtitah/
Ekadantaavataaro vai dehaanaam
Madaasurasya hantaa sa aakhuvaaha -nagah
Mahodara iti khyaato Jnaana Brahma prakaashakah,
Mohaasurasya shatruvaim aakhu- vaahanagah smritah/
vigjneyah saankhebhyah siddhi daayakah,
Lobhaasura prahartaa vai
Lambovataaro vai Krodhaasura
Shakti Brahmaakhugah sad yat tasya dhaaraka
Vikato naama vikhyaatah Kaamaasura vidaahakah,
vaahanash -chaayam Sourabrahmadharah smritah/
shesha vaahana uchyate,
Mamata--asura hantaa cha Vishnubrahmoti
Dhumra varnaavataarascha abhimaanaasura naashakah,
akhuvaahana evaasou Shivaatmaatu sa uchyate ||
Vakratunda sporting the back on a roaring lion killed Matsaraasura.
Seated comfortalby as a ‘mooshaka vaahana’, the Lord with His
‘ekadanta’ the single tusk destroyed Madaasura. Mooshaka vahana
Ganesha as manifested as Mahodara killed Mohaasura.Assuming the title
of Gajaanana killed Lobhaasura while as Lambodara destroyed
Krodhaasura. The outstanding evil of the Society viz. Kaamaasura was
subdued and killed by Ganesha as Mayura Vahana while as Sesha Vahana
Vighna Raja killed Mamataasura. As Mooshaka Vaahana, Maha Ganesha
destroyed Abhimaanaasura. Thus as Vakratunda-Ekadanta and such
‘avataaraas’, Ganesha destroyed Matsara, Mada, Moha, Lobha, Krodha,
Kaama, Mamata and Ahankaara naamaka asuras.
So as Vakratunda he killed Matsarasura, as Ekadanta Madasura etc.
(Note - The author of the cited article is the same person who's books get published on the Kamakoti.org. All the "Essence of Purana Series" books are authored by him.)