Well, let's considering what you're asking here.
You're asking if people who code think differently. Well, let's consider those who know how to program. Some people plan what they are going to do, while others take a more dynamic approach. Some people create a 'skeleton' of what they are about to build before they fill in the missing pieces (and will debug each piece as they go), and yet others will create one new method at a time until they have one giant bug-filled product to deal with at the end.
Now pick two arbitrary coders. Do they think differently from each other? Probably. They probably have different approaches, interests, strengths, and weaknesses. But sure, they probably think differently than, say, someone who works in a grocery store.
But then again, take the person who works in a grocery store. They probably have different methods for dealing with shoppers, they probably use different greetings, they may have different strengths and weaknesses, etc.
In fact, I would argue that in instances where you are given a choice, it isn't what you do that teaches you to think; rather, the way you think determines what you do. You may pick up on certain methods out of habit (maybe you see people as variables, or maybe you're quick to decompose your thoughts like you would a program), but on top of learning new skills, those habits you pick up are probably further emphasizing the ways in which you currently think.