How do you know when an option is “deep” ITM/OTM vs just ITM/OTM?

There's no fixed rule for when an option officially can be considered "deep” ITM/OTM vs just being "ITM/OTM", but you can apply common sense to make that judgement yourself. For example, if the strike price is 10% away from the underlying, that's considered quite deep. But if the strike price is only 1-2% away, that's just ITM/OTM and not necessarily deep, since stocks tend to fluctuate a couple % daily and it could easily get knocked back into the opposite territory. Basically, the question to ask yourself is "How likely is it that this option will go from ITM to OTM or vice versa?" If the only way the option would end up in the opposite territory is if the underlying stock experienced a number of out-of-the-ordinary trading days, then that option is definitely “deep” ITM/OTM.