Off-market strictly means the property isn't listed on the MLS, the multiple listing service that agents use to publish inventory. That's the tight definition and it's the one worth holding onto. Loosely, people also use it to mean "the owner hasn't decided to sell," which is a different situation, sometimes called a pre-market or pocket situation. Both are off-market under the strict definition, but only one of them has a seller who's ready to sign, so it matters which you're looking at.
Distressed splits the same way. Physically distressed means the building needs work. Financially or situationally distressed means the owner needs an exit, from probate, divorce, a tax problem, or a carrying cost they can't hold. The person who told you it's often a situation rather than a building isn't wrong, and the $180k kitchen isn't wrong either. Plenty of luxury deals are one, some are both, and the both category is where the large fees tend to sit, because that's where the discount comes from two directions.
As for finding them, at this price level it runs through people. Estate attorneys, trust officers, high-end contractors who've bid a job the owner then abandoned, agents whose listing expired. Direct mail works less well because the owner of a $3m house has staff and filters.
Something you'll want to sort out early: you can find one of these and be unable to do anything with it, because the end buyer for a distressed $2m house is a specific and rare person. Start on the buyer side before the sourcing side, or you'll be holding a contract with a deposit on it and nobody to hand it to.
