XI has:

Terrestrial Avatars (Carbuncle, Diabolos, Fenrir, Phoenix and Bahamut)
Celestial Avatars (Ifrit, Shiva, Garuda, Titan, Leviathan, Ramuh)
Temporal Avatar (Atomos)
Tears of the Goddess (The 9 Cait Siths.)
(Odin and Alexander)

The gods of FFXI were Promathia and Altana (I forgot who Aht Urghan believed in, but it wasn't Altana), whom we don't summon at all in any way. The terrestrial avatars you had to do a bit more work to summon compared to the celestial avatars, but even then the story dictated you summoned a fraction of their power as a summoner, but they may be gods, they're not actual gods, the world isn't technically governed by them.


XIV's universe has a different type of god sets, for example the Twelve are gods/goddesses in the light of Promathia and Altana, so summoning them wouldn't make much sense, but the Primals are considered false gods but they're also the "main" summons from the series, which is why they're going to make it a Free Company type of deal, but for summoners they will get lesser summons like Carbuncle as yoshida exampled.