Practicing a Profession is one of the ways to spend your downtime. Specifically, it's a way to spend your downtime without paying a fee (provided you want to maintain a comfortable lifestyle). If you practice a profession in town, you can lead a modest, comfortable or wealthy one (depending on circumstance), if you do so out of town, you can lead a poor one (unless proficient in survival which allows comfortable).
If you don't want to work, and want to spend your downtime doing something else (or nothing at all), you must pay for whatever lifestyle you want to afford. So if you don't want to pay, you'll lead a Wretched lifestyle, with the benefits and penalties that come with that (and trust me, there will be serious penalties to doing this longterm).
Lifestyle expenses are listed in the chapter 5 of both the PHB and BD&D rules (p 157 of the PHB, p 53 of BD&D). They are also described there. The rules are effectively, you are considered to live the lifestyle you pay for (though the Adventurer's league is a bit more strict, to drop you only have to spend 1 night living the lower lifestyle, but to increase you must spend 30 days paying for it).
As far as living in the wild without practicing a profession, you'll still need to pay for a lifestyle then, because "practicing a profession" in the wild represents the things you need to do to survive, if you're not spending time catching food, maintaining your tools and habitat, you're going to have to pay someone else to do so if you want to maintain a specific standard of living. Otherwise you're living conditions are considered wretched and you would be subject to whatever conditions the DM wills on you (likely disease and bandits on a frequent basis).