What optical illusion is this?

It demonstrates simultaneous (induced) contrast. Every grey circle on the board is exactly the same shade at any instant, but the human visual system judges brightness relative to the surrounding area, so a circle on a dark square looks lighter while the identical circle on a light square looks darker.

Are the circles really all the same colour?

Yes. All circles are filled with one identical grey value that pulses over time. Only the black or white square beneath each circle changes how light or dark it appears — the circles themselves never differ from one another.

How can I prove the circles are the same?

Press Reveal the Truth. The checkerboard fades to one flat colour while the circles keep pulsing, and with nothing different underneath them every circle is plainly the same grey. Press it again to bring the illusion back.

Open the settings cog to change the board mode (static, crossfading or a rotating split), the number of columns and rows, the flash speed of the circles, the board speed, and the amount of blur on the circle edges.

Induced Contrast Checkerboard — Interactive Optical Illusion

Some circles look lighter, some darker. They are all the same grey.