I don’t know anything about pools (coming from a country where an outdoor pool is unusable for 11 months of the year

) but I usually find that fixings supplied with products are totally inadequate for the purpose.
If you’re fixing into concrete, or concrete block, the best option is a Rawlbolt / concrete anchor. These are unbelievably strong provided you’re fixing it into something solid.
Other options are a “Tapcon”, that screws straight into concrete
Or a chemical anchor
Both of which work better than they look like they might.
If whatever you’re fixing has small holes, and you have to use screws, then use a decent wall plug.They all look similar but the quality varies enourmously.
If you have the space, some manufacturers (e.g. Fischer) offer extra long ones.
And use a coach screw / lag screw rather than a regular screw. Stronger and easier.
Finally, you will find that concrete, with gravel in the mix, can be very hard on drill bits. I’ve seen cheap ones wear out before making it to the bottom of one hole, so give yourself a fair chance and get something decent. Even good ones are not expensive.
If you are drilling into concrete, get a proper SDS drill. Even an inexpensive one will work waaay better than any other option.
I suspect that cherrybomb was suggesting that pool railings get leant on and hauled on, so you don’t want the fastenings failing. Same applies if you’re fitting a grab handle by a step, or in a shower for an elderly person.