As far as I am aware, in the Nasuverse, “god” and “divine spirit” are synonymous.
Divine spirits can’t usually be summoned, because they don’t exist in the Throne of Heroes (where the summoned servants come from). However, it is possible for a divine spirit to make themselves summonable, should they wish to, though that requires them to sacrifice a great deal of their power, since the servant containers can’t handle their full divine Authority. This is essentially what Tamamo did, for example.
In the case of Saver in Fate Extra, that was a special case, in that it was the nature of the summoner’s desires and struggle that motivated him to answer the summons. In short, Saver was interested in seeing how this situation would play out, and decided to come, himself.
It should be noted, however, that the normal HGW summoning ritual (from F/SN), the Mooncell (from Fate/Extra), and the Fate system (from FGO) all function differently, and don’t necessarily share the same limitations.