Why the difference in band prices? And rose gold colors?

I would read things very carefully if you're finding that they vary in prices that greatly. First thing I thought of was whether it's solid rose gold or rose gold plated (some other metal coated in rose gold). It also matters if its 10k, 14k, or 18k rose gold in terms of price and quality. You also have to consider width as well.

Exactly this. Anything gold plated will be much cheaper, but it will also tarnish. Make sure you do your research, especially if you are ordering online.

Several possibilities:

Gold versus gold plated, as discussed above.

Karats. Since it looks like you're only considering 14K, this wouldn't be the difference in your case. A 10K ring would be a different color from an 18K, but two 14K should be about the same color.

Width. A 2mm band will be less than a 5mm band, for example.

Weight/thickness. This is basically how high it is, when you have your hand flat on a table. A heavier/thicker band has more gold in it, so is more expensive.

But it's also true that a ring from a brick and mortar store will be more expensive than one from an online only store. And one from a high end store will be more than one from a lower end store.

Another thing you can consider is getting a used ring on eBay. That may save you money, and a quick polish will make it look new.