You can manage risk very well by always having a stop in the market, and never moving it, so that you're always stopped out where you want to be. But trust me, I know, this isn't enough to make money. You also need the right target, and you also need it to hit often enough.
The edge is the side of a knife you use to slice a whole in other traders's trousers to empty their pockets.
Don't get confused, or obsessed, with terminology and other fluff words of lingo; Just trade good, or trade bad. -- whatever that may personally mean to you. Alot of things in life...are relatively simple, but for some reason...it blossoms into an overly complicated thing.
My edge is not setting a stop-loss and only trading positions that align with my long-term outlook. That is, buying low and holding until it pays off with an instrument like the GBPJPY. The nice thing about leverage is I can carry over my losers until they become winners, if there's a massive move down I can sit on it and if my long-term outlook changes I can liquidate. The only problem is getting swamped with mod-term positions.
An edge in trading is a "competitive advantage" you have in the market to derive long-term profits from buy and sell activities. This can be ANYTHING that gives you an advantage.
Easier to say than do. The reality is that you have to define good and bad to succeed. It's a monumental task that most people aren't wired for.
An edge means you have a good strategy. Most strategies are shit because they have a negative edge meaning over 100 trades, you lose more trades than you win, or your risk reward is 1:1 or less than 1:1. A positive edge means your strike rate over 100 trades is more than 50 wins, or that your risk to reward is 1:2 or 1:3 and up. Edge means you either win win more trades in strike rate or have a higher risk to reward. Very simple.