A spectroscope is a device to study light's spectrum. The terms spectroscope, spectrograph, and spectrometer now are used interchangeably for advanced instruments.
The term spectroscope was given to a device that allows you to look at a spectrum, much like a telescope or microscope that also includes a prism or grating and a built-in visible scale to assist you identifying the wavelengths of spectral lines. The term spectrograph was used for devices much like a spectroscope attached to a camera, that focus the spectrum on photographic film, recording it for later study. The term spectrometer has always been a general term that encompasses either.
Modern advanced instruments virtually always focus the spectrum on a CCD or similar sensor, allowing the spectral data to be transmitted, recorded and analyzed electronically, and all three terms are commonly used for such instruments. The terms may be used for analyzers of any part of the electromagnetic radiation spectrum, but when used for other than visible light, that is often mentioned, e.g., the phrase "X-ray spectrometer".