You're right about the manual versus the bulbs installed. I'm guessing the
3057 is installed to make more of a difference between bright and dim than the 3157.
Here's a quick guide for the brightness of a few different types of bulbs that will fit:
3057 - tail (dim) 2CP, stop/turn (bright) 32CP
3157 - tail (dim) 3CP, stop/turn (bright) 32CP
3457 - tail (dim) 3CP, stop/turn (bright) 40CP
Any of these will work. I like to use 3457 bulbs myself, as the stop and turn is brighter, and makes more of an impact to the people on the phone behind me.
The "K" suffix means that the bulb is filled with krypton gas, which can extend the life of the bulb. You can usually find the "K" bulbs from Sylvania.