One significant difference in interpretation that layfolks do consider important is that it's possible to exit from within the event horizon of a black hole in Newtonian gravity (without exceeding the speed of light) whereas in general relativity that is not possible.

In relativity the event horizon really is a point of no return, whereas in Newtonian physics it's the point at which escape velocity is equal to the speed of light. The escape velocity on the surface of the Earth is 11 km/s, but that doesn't mean that I as a human can't escape the surface of the Earth momentarily just by jumping and I certainly don't jump 11 km/s or even 1 km/s for that matter.

Similarly in Newtonian gravity it would be possible for an object to enter the event horizon of a black hole, and then "jump" back out at a much lower speed than the speed of light and then get sucked back beyond the event horizon, and you can in principle do this over and over again so long as you had some sufficiently powerful source of thrust.

In general relativity this is in principle not possible.