No, the H4 and 9006 bulbs are not the same.
The 9006 bulb is a single-filament bulb with an L-shaped base.
The H4 bulb is a double-filament bulb that features three prongs.
A similarity that these two bulb types share is that they can both be used as headlight bulbs producing high (H4) or low-beam (9006) lights.