Miracast is "effectively a wireless HDMI cable, copying everything from one screen to another using the H.264 codec and its own digital rights management (DRM) layer emulating the HDMI system".
So, no, the Miracast protocol is not the same as HDMI, assuming this statement is correct. The HDMI data is sampled and compressed (H.264), transmitted to the received, and decoded back to HDMI. This also means that the compression is lossy.