This is something I'm genuinely still working on, and it's one of the bigger adjustments I've had to face coming from a tournament background.
In tournaments, deep stack play only really happens in the early levels before the blinds eat into everyone's stack. So my experience with truly deep stacked situations is limited. In cash games, you can be sitting with 150, 200, even 300 big blinds, and the game changes in ways I'm still learning to navigate.
The most obvious difference I've noticed is that speculative hands go way up in value when stacks are deep. Suited connectors, small pairs, even suited one-gappers become much more interesting because the implied odds are huge — if you hit a disguised hand against someone who has a big stack and a strong but second-best hand, you can win a massive pot.
On the other hand, hands like top pair top kicker become trickier to play for big pots when stacks are very deep. In tournaments I'd often be happy to get it in with TPTK, but in a deep cash game that same hand can easily be in bad shape by the river if the pot gets huge.
Honestly, I'm still at the stage where I know the theory but don't always apply it correctly in real time. I sometimes find myself playing deep stacked situations too similarly to how I'd play in a tournament, which I know isn't right.