Greetings AJ,
The light-colored wood you refer to is termed "sapwood". In eastern black walnut (Juglans nigra), there are commonly 10-20 annual growth rings in the sapwood. To the inside of the sapwood is "heartwood". As the girth of the tree increases with the addition of new sapwood, the diameter of the heartwood zone also expands proportionately (from Hoadley 1990).
According to Brown and Panshin (1940), sapwood is usually much easier to season and takes preservatives more readily. Therefore, your walnut lumber will take stain differently in areas of sapwood and heartwood. Thus, you may want to employ various methods to reduce this effect…say stain the sapwood and not stain the heartwood…stain and wipe…etc. I don’t profess to be a woodworker, so you’ll have to do a little internet searching regarding the best methods to match-up sapwood with heartwood – if this is indeed the look you are after.
Depending on who you talk to or who you are selling to, sapwood may or may not be regarded as a defect. In the veneer industry, sapwood is generally regarded as a defect and is often removed in the final processing stages. Furthermore, many black walnut logs are soaked and steamed in large vats at the veneer mill to accept the darker color of the heartwood.