Because the RX 580 itself draws 185w, I thought the NITRO might use more since its clocked higher and has more features. I havent bought anything yet. All I have is my HDD and RAM at the moment, so do I need to buy a power connector separatley from the PSU (Im getting a Cooler Master 550w PSU which is probably enough for Ryzen 5 + Rx 580). Also, if they both use the same amount of power, why does one have more PIN connectors?
Don't confuse the TDP limit with actual power usage. The RX 580 has a TDP of 185w, this isn't to say it's peaks can't exceed that, but typically it won't consume that much power. As I already said, the Nitro will probably draw more power than the Pulse as it's clocked higher, but this doesn't mean it will be over the TDP of 185w.
Your new PSU will come with all the power leads you need, so no, you don't need to buy any extra connectors. The PSU will have at least 2 PCIe power leads, probably as 6+2 connectors, which can be used as both a 6 pin or an 8 pin.
As for why it uses an extra connector; Card manufactures must decide how they want to power their cards, some may make the motherboard supply the maximum 75w the PCIe slot can provide, and supply the rest through another power connector. While a different manufacturer may include two connectors and draw most of the power from them and not so much from the slot. In general, it's better to have more power supplied than what's needed so that there is headroom for overclock, without risking overloading anything.