yes; the motherboard is the board and chips that connect your CPU (the main chip, that does all the computations) to everything else, such as the display, the mouse, the keyboard, and the hard drive.
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It is not a "type", they are proprietary designs shaped to fit within the designer's choice of custom case, having cutouts ample for the amount of cooling a given generation of parts needs, the amount of plug-in peripherals, the size of the battery they choose for that system design, etc. The only type a type, as-in compatiblity would be important is replacing the board and to do this you need to compare them visually to other similar models from the same manufacturer, and if a different generation of system, also considering whether they use the same CPU and memory technology if those parts are to be reused, and that the total power consumption stays within the maximum the AC-DC power brick is capable of or else you will have to replace it too.