So the two methods are:
1) Request authentication from a perviously authorized device. This means that the iCloud Keychain system will send a pop-up to all of your devices currently already using iCloud Keychain and authenticated. This is the easiest method, because it will simply pop-up on your other device(s) and have you authenticate with your Apple ID password to give your new device access. Done.
2) Use security Code & Device Verification Code. This is where you enter your security code you created for iCloud Keychain and then enter the secondary authentication number received (usually via SMS). This method its for those who may have a backup plan to the first option. Like in my case, I have SMS authentication going to my phone number and my wife's phone number. While my wife is not accessing my iCloud Keychain, I can use her as an authentication point in case I can't do option #1.
In your case, you are obviously able to do both options with your iPhone because its authenticated in iCloud Keychain (already utilizing the service) as well as set up for the secondary SMS verification.
Well, I hope that explains why there are two options and who they might be utilized differently. At the end of the day, it allows multiple options for different scenarios.
Frequently asked questions about iCloud Keychain - Apple Support