The goal of a seismic sensor is to monitor Earth vibrations. It can be based on an accelerometer specifically designed for this application. But accelerometers can be designed for other applications, such as airbag sensing. In this case, they are not seismic sensors. Also, principles different than accelerometers may be used for developing seismic sensors.
The first seismic sensors that I'm aware of were acoustic. It was mentioned in a Chinese document from somewhere around 400 BC, and was designed to detect intruders.