The graphics card (driver?) does the same exact thing.

Also note that SDL 1.3 (now known as 2) renders with OpenGL

1. No, it doesn't. It's a completely different thing.

2. Yes, but as I am trying to point out, there is a huge difference between e.g. glDrawPixels and glDrawElements.

One is deprecated OpenGL 1.2 functionality, which is an entirely different pipeline (with kernels, color matrix and whatnot, see imaging subset) that has always been kind of of half-heartedly supported.
The other is the fully accelerated, native way of drawing textured geometry (such as a quad) using dedicated hardware.
Which, on my system, makes a difference of roughly 1 to 10. Your mileage may vary.

The graphics card (driver?) does the same exact thing.

Also note that SDL 1.3 (now known as 2) renders with OpenGL

1. No, it doesn't. It's a completely different thing.

2. Yes, but as I am trying to point out, there is a huge difference between e.g. glDrawPixels and glDrawElements. One is deprecated OpenGL 1.2 functionality, which is an entirely different pipeline (with kernels, color matrix and whatnot, see imaging subset) that has always been kind of of half-heartedly supported.
The other is the fully accelerated, native way of drawing textured geometry (such as a quad) using dedicated hardware.
Which, on my system, makes a difference of roughly 1 to 10. Your mileage may vary.