I understand the confusion now. Only the starting sector is visible at the start of the game, which can be Tiny, Small, Medium, or Large in size. Once you do the research that allows you to see and travel the subspace streams, the rest of the sectors in the galaxy will be available to you. There can be a lot of sectors in a very large galaxy, depending on your choices at the start of the game.
All the sectors fit in a "galaxy" that is made like the galaxies in GalCiv3, but only the area in the sectors is usable in GalCiv4 until a late tech is researched that allows travel between sectors without using the subspace streams. That tech is not active in the 0.60 alpha.
I'm not sure how the sizes of the sectors compare to the sizes of the galaxies in GalCiv3.
For the largest galaxy, all the sectors fit in a "galaxy" that is more than five times the size of the largest (ludicrous) sized galaxy in GalCiv3, so the area in the sectors is very large.