There are 512 tiles in memory on NES. One can consider them as two separate 256 tile sets. Usually one set is used for sprites, and one set is used for the background. (It's possible to use the first set for both sprites AND the background, and it's possible to use the second set for both sprites AND the background, but this isn't common. Why opt for 256 tiles for EVERYTHING when you can use 256 tiles for sprites, and 256 tiles for the background?) Which set is used for which thing can be set at ANY time.
You CANNOT access the sprite tiles when drawing the background AT ALL. Say the first set is the background set, and the second set is the sprite set. You CAN say, "set two is now the background set" to draw some sprite tiles in the background. But you can only render from the second set while that's true. You can't place say... your main character's head from the sprite set in between other background tiles in the same row. You'd need to duplicate your main character's head in the background set to do that.
Sprites CAN use the background side, but only if the NES is set to use 8x16 sprites. Then, any sprite can be drawn with two background tiles as well. Since an NES character is usually larger than a single sprite, it is possible to have one character use tiles from both the background and the sprite set. It's not even hard to do.
So if you were using only say... 100 background tiles in a level, and wanted to use the rest of the background set to store more sprite animation, you could, if you were using 8x16 sprites.
There are no "sets" the NES cares about beyond what's described above, there are no rules for where things must be beyond what's described above. Games copy (OR map) their graphical data into these sets. Before the data is copied into NES memory, it can be stored in any way, in any order. It can even be randomly generated rather than stored. Anything, truly anything. NES only cares about its 512 tiles in memory. How the tiles get there, or what bank they were in before they got there is not its concern at all.
(Technical caveat! If a game is using CHR ROM, graphical organization is less free. But NES Maker is NOT CHR ROM.)