Risk arbitrage differs from pure arbitrage in that it involves risk, whereas pure arbitrage seeks to lock in a guaranteed profit the moment trades are initiated. But the risks involved in risk arbitrage are calculated risks that, when done correctly, can be tilted in the trader's favor.
The essence of the no-arbitrage restrictions is that in an n-factor model, the mapping from one bond's yield to the n factors can be written in terms of similar mappings for n + 1 other “base” bonds. (We need n + 1 bonds instead of n because the restrictions are tied to expected excess returns, not expected returns.)
Short Answer Equilibrium models focus on market balance; no-arbitrage models ensure no profit from arbitrage opportunities.
There are multiple methods to find arbitrage bets - these are manual searching in the right markets, creating synthetic arbitrage bets which is what I teach in my course and using odds scraping software or arbitrage software to detect arbitrage bet opportunities.