You are counting 27 because you are counting actions that are all overlapping on certain actions.

Without role actions (Addle, Swiftcast, Sleep, Lucid Dreaming, Surecast) and Physick:

1.) Ruin III -> [Astral Impulse / Fountain of Fire]
2.) Tri-Disaster -> [Astral Flare / Brand of Purgatory]
3.) Gemshine -> [Ruby Rite / Topaz Rite / Emerald Rite]
4.) Precious Brilliance -> [Ruby Catastrophe / Topaz Catastrophe / Emerald Catastrophe]
5 + 6.) Energy Drain, Energy Siphon
7 + 8.) Fester, Painflare
9, 10, 11.) Summon Ifrit / Titan / Garuda II
12.) Astral Flow -> [Crimson Cyclone + Crimson Strike / Mountain Buster / Slipstream / Deathflare / Rekindle]
13.) [Summon Bahamut / Summon Phoenix]
14.) [Enkindle Bahamut: Akh Morn / Enkindle Phoenix: Revelation]
15.) Radiant Aegis
16.) Resurrection
17.) Searing Light
18.) Ruin IV

Summoner has 18 unique buttons to press, not accounting for single-target vs AOE scenarios.