This might be a question with a stupidly easy answer:
I have been casually using all of the adobe products for awhile. Although I have used Illustrator and InDesign the most, I occasionally use Photoshop.
My question: when I am making something in photoshop, the background of the board sporadically changes between grey/white squares and a grey background – what is the purpose of this and how do I make it so that it stays a consistent color?
Transparency is indicated by the transparency grid (grey and white squares). If you have no transparency, then you don’t see the grid.
Your top image has the canvas cropped to the size of the artwork, so what you see outside the artwork is the window background. The bottom image has a transparent canvas much larger than the artwork, so the transparent canvas is indicated by the grid.