Are there different shittas as to when shkia is?
No. Anyone can look at the horizon and see when the sun sets.
That’s if you go according to the Gaonim, who consider “shkiah” the setting of the actual sphere of the sun.
Rabbeinu Tam, however, considers “shkiah” to be when the last rays of the sun “set” (also called “shkiah shniyah”).
Since many follow R”T’s shittah (some Chassidim), one shul can be davening Mincha while another is davening Ma’ariv.