Short answer:
As per this shloka (which you quoted in question), 18 Mahaapuraanas are:

- Madwayam: 1. Maarkendya, 2. Matsya
- Bhadwayam: 3. Bhavishya, 4. Bhaagavat
- Bratrayam: 5. Brahma, 6. Brahmaanda, 7. Brahmavaivarta
- Vachatusthayam: 8. Vaamana, 9. Vishnu, 10. Varaaha, 11. Vaayu*
- ANaPaLinGa KuSkani: 12. Agni, 13. Naarada, 14. Padma, 15. Linga, 16. Garuda, 17. Kurma, 18. Skanda
*In the above list, many scholars (e.g. this answer and this comment) consider that Vaayu Puraana includes Shiva Puraana as well which is partially supported by Matsya Puraana: Chapter 53.
The list which consider Vaayu and Shiva puraana as one unit seems to be more common but all mention count as 18.
But if we count them separately then the count is 19 or even 20 as few consider Vishnudharmottara the second part of Vishnu Puraana (as asked here) or even 21 as few consider Harivamsha too (as mentioned in wikibooks) or even 22 as few consider Devi Bhagavatam too (though mostly classified as Up-purana but few argue it to be in place of Bhagavta but few say both coexist as asked/answered here) or even more as there might be some more such examples. But the Puraanas themselves mention the count only 18.
Long answer:
- As per Vishnu Puarana: Part 3: Chapter 6, the 18 Mahaapuraanas are (I have changed the order to compare, actual order in bracket):

- Maarkendya (7), 2. Matsya (16)
- Bhavishya (9), 4. Bhaagavata (5)
- Brahma (1), 6. Brahmaanda (18), 7. Brahmavaivarta (10)
- Vaamana (14), 9. Vishnu (3), 10. Varaaha (12), 11. Shiva (4)
- Agni (8), 13. Naarada (6), 14. Padma (2), 15. Linga (11), 16. Garuda (17), 17. Kurma (15), 18. Skanda (13)
NOTE: In above list, Shiva Puraana replaces Vaayu.
- As per Brahamavaivarta Puraana: SriKrsna-janma-Khandam: Chapter 133, the 18 Mahaapuraanas (with number of verses) are (I have changed the order to compare, actual order in bracket):
- Maarkendya (7), 2. Matsya (16)
- Bhavishya (9), 4. Bhaagavata (5)
- Brahma (1), 6. Brahmaanda (18), 7. Brahmavaivarta (10)
- Vaamana (14), 9. Vishnu (3), 10. Varaaha (12), 11. Shiva (4)
- Agni (8), 13. Naarada (6), 14. Padma (2), 15. Linga (11), 16. Garuda (17), 17. Kurma (15), 18. Skanda (13)
NOTE: In above list, Shiva Puraana replaces Vaayu.
- As per Śrīmad-Bhāgavatam (Bhāgavata Purāṇa): Skandha 12: CHAPTER THIRTEEN, the 18 Mahaapuraanas (with number of verses) are (I have changed the order to compare, actual order in bracket):
- Maarkendya (7), 2. Matsya (16)
- Bhavishya (9), 4. Bhaagavata (5)
- Brahma (1), 6. Brahmaanda (18), 7. Brahmavaivarta (10)
- Vaamana (14), 9. Vishnu (3), 10. Varaaha (12), 11. Shiva (4)
- Agni (8), 13. Naarada (6), 14. Padma (2), 15. Linga (11), 16. Garuda (17), 17. Kurma (15), 18. Skanda (13)
NOTE: In above list, Shiva Puraana replaces Vaayu.
- As per Matsya Puraana: Chapter 53, the 18 Mahaapuraanas (with number of verses and merit of their donation) are (I have changed the order to compare, actual order in bracket)::
- Maarkendya (7), 2. Matsya (16)
- Bhavishya (9), 4. Bhaagavata (5)
- Brahma (1), 6. Brahmaanda (18), 7. Brahmavaivarta (10)
- Vaamana (14), 9. Vishnu (3), 10. Varaaha (12), 11. Vaayu* (4)
- Agni (8), 13. Naarada (6), 14. Padma (2), 15. Linga (11), 16. Garuda (17), 17. Kurma (15), 18. Skanda (13)
NOTE: *The text mentions with the glory of Rudra. Due to this many translate it as Vaayu Puraana along with Shiva Puraana. This list matches with the list mentioned in the first part (short answer).
Below are the different lists from the above concept:
- As per Kurma Puraana: Purvardha: Chapter 1:

- Maarkendya (8), 2. Matsya (16)
- Bhavishya (6), 4. Bhaagavata (5)
- Brahma (1), 6. Shiva (4), 7. Brahmavaivarta (10)
- Vaamana (14), 9. Vishnu (3), 10. Varaaha (12), 11. Vayu (18)
- Agni (9), 13. Naarada (7), 14. Padma (2), 15. Linga (11), 16. Garuda (17), 17. Kurma (15), 18. Skanda (13)
NOTE: In above list, Brahmaanda Puraana is not included (or Shiva Puraana replaces Brahmaanda) but all 18 puraanas are collectively called as Brahmanda.
- The list by IGS (International Gita Society) mention below 18 Mahaapuraanas:
- Maarkendya (6), 2. Matsya (15)
- Bhavishya (17), 4. Bhaagavata (10)
- Brahma (1), 6. Brahmanda (18), 7. Shiva (4)
- Vaamana (5), 9. Vishnu (3), 10. Varaaha (7), 11. Vaayu (16)
- Agni (8), 13. Naarada (12), 14. Padma (2), 15. Linga (11), 16. Garuda (14), 17. Kurma (9), 18. Skanda (13)
NOTE: In above list, Brahmavaivarta is not included in the list (or Shiva Puraana replaces Brahmavaivarta).
- The list by wikipedia page on Puranas, mention below 18 Mahaapuraanas:
- Maarkendya (9), 2. Matsya (10)
- Shiva (13), 4. Bhaagavata (2)
- Brahma (3), 6. Brahmaanda (4), 7. Brahmavaivarta (5)
- Vaamana (15), 9. Vishnu (18), 10. Varaaha (16), 11. Vayu (17)
- Agni (1), 13. Naarada (11), 14. Padma (12), 15. Linga (8), 16. Garuda (6), 17. Kurma (7), 18. Skanda (14)
NOTE: In above list, Bhavishya Puraana is not included in the list (or Shiva Puraana replaces Bhavishya).