I do not believe Paul is making a distinction between walking in the Spirit and living in the Spirit.
In our speech and writings we typically use different words to say the same thing. In normal speech and writing people tend to avoid repeating words or phrases to convey a thought. It's just awkward.
Unless you are a Democrat, then it's common.
Seriously, though. Think about it.
"I have an amalgamation of chemicals. What do I do with this amalgamation of chemicals?" vs "I have an amalgamation of chemicals. What do I do with this mixture?".