HDMI Matrix: Connecting multiple HD devices to multiple HDTVs. HDMI Matrix or HDMI Distributor,They are combining the functions of input and output switches, they receive multiple HD signals and output to multiple displays.The first time I wanted to hook up PLC splitter my Xbox360, HTPC and Blu-ray player to my old HDTV which had only 1 HDMI port left, I didn't know what device I should be looking for.

Unfortunately, none of them were the popular names. This is what you need when you want to hook up all your PS3, BluRay, HD PVR, etc all to a single HDMI port on your HDTV because your HDTV has only 1 port left.

They are the names of an HDMI input switch, which receives signals from multiple HD devices, and output to only 1 HDMI port on an HDTV, monitor or projector.

HDMI Adapter: Connecting HDMI port to another type of video port. This is what you need when you want to output the same HD signal to 2 or more HDTVs.

Such a product is actually commonly called an HDMI switch or HDMI switcher. HDMI Splitter or HDMI Amplifier
In contrast, they are the names of an HDMI output switch, which receives signals from just 1 HD device and outputs to 2 or more HDTVs or monitors. I know what splice tray I want it to do for me, but I don't know how to call it for me to google it.

They are rarely used by average consumers but more commonly used by electronics stores or exhibition hosts who need to display many screens simultaneously with HD signals coming from several devices. HDMI Adapter or HDMI Converter
These are very general names, which, however, usually mean a much simpler device that connects HDMI port to another video port such as a VGA or DVI port.

After reading this article, you will get a much clearer picture of the common names of the many HDMI gadgets and what they do. Of course, there is no official name for it, but there are names more commonly used than others by the majority of the users.