Execute basics like making a good product, answering your customer emails, keeping up on the utilities, etc. Basics you know you'll have to do regardless of strategy.
If you're in the wrong market or building for the wrong customers you can execute brilliantly on everything you mentioned and it won't matter. The only thing that matters is product market fit or finding it if you don't have it. That's what I see as unsaid in your parent's comment about "execute what though?"
If I'm running a lawn care company in the desert I can get all those annoying details right and still be unsuccessful. So strategy is not opening a lawn care company in the desert.
If you think I'm missing something you are saying, please let me know!
So maybe there's "strategy" on the level of "sell something that non-zero people want", then there's execution on the details, and then a higher level of strategy that's maybe related to fine tuning product market fit, etc. But that feels like a weird discontinuity in "strategy" along the priority axis, and definitely doesn't fit with the conventional tone of "strategic thinking", which is definitely more on the "higher" level end of that spectrum.
Strategy is about choosing how to achieve a goal, all the tactics, fitness measures/metrics, compromises, challenges to overcome but it's also the goal itself. Strategy should guide you, your tactics at play to deliver your ultimate goal. Execution is just doing that stuff hopefully focussing on the stuff that matters most.