"Wild" is as opposed to farm raised. From a purely statistical stand point, you simply don't get the diversity in genetic background in a farm environment. This leads to both more static taste (good for masses, not what I'm looking for) and higher likelihood of diseased/medicated food product.
"Organic" is as good as the brand behind it. I'll tend to err on the side of organic but not put a ton of value into that label unless I've researched the company behind it and how/where they do business. I'm looking for fresh as much as I'm looking for organic. Maybe that company figured out some packaging to make their food last a little longer but still allow them to keep the organic label. I'm still losing versus something I just bought off a farm.
To me, those labels aren't as important as the type of food that I'm eating in the first place. While the political vegans/veggies garner the higher pub, I think the vast majority of people who come to a healthier/more well thought out diet do so more quietly out of some simple necessity that confronts them at some point in life. If you don't ever get sick and don't ever get too fat/too thin, then there won't be much motivation to change.
For me, the point came about 5-6 years ago when several medical problems came to a head for me for which none of a line of doctors could pin point a treatable solution. Since that point, I've slowly migrated my diet from one of whatever I felt like to very high in fruits in vegetables, followed by one meat protein a day and the very occasional grain or nut. I'm also on a very big garlic/oregano/ginger kick right now. And to speak to skeeter's point, yes, there was a lot of balancing of cravings during that time. I used to have to fight to not eat the free office bagels on Thursday. Now they don't even look like food to me because I know what happens to my day when I have one.
My diet excludes processed food almost entirely. This includes the trendy vegetarian staples of tempeh, tofu and the like. If I want chicken, I eat chicken, not a frozen TV chicken dinner. Five years ago, I didn't think much of the difference. Now I do because I can feel it in my system and (pardon the honesty) see it in my shit. I've come to the point where I literally feel the difference between something that is processed and something that is wild/fresh/organic without needing a label. There are so many degrees even within those labels that I depend much more on my own taste. If eating healthfully is something you want to make important to you, I think it's much more a matter of training that taste than worrying about what labels say.
It is easy to buy small plaster models of what you think life is like.