Astronomy and astrophysics are very closely related topics. For most purposes the terms can be used interchangeably and only a pedant would try to tease out the difference. Both subjects are concerned with the study of matter and energy outside the Earth’s atmosphere.
Historically, astronomy is the older science dating back to antiquity whereas astrophysics is a new term coined only in the twentieth century. Astronomy has a rich heritage of observation and experimental technique. An old fashioned astronomy was concerned with the painstaking logging of the heavens. It was very painstaking and exacting work. With the development of the subject astronomy has become much more dependent upon physics both in terms of sophisticated observational techniques and in terms of understanding the objects and processes that are under study. Observational techniques now extend across the full range of the electromagnetic spectrum from gamma rays to x-ray astronomy to infra red to visible and to radio waves. Although heavily dependent upon observational techniques based upon the electromagnetic spectrum astronomers are extending their studies to include gravitational waves and neutrino emissions. Astrophysics could well be thought of as the modern name for astronomy.
In terms of education the vast majority of astronomers receive their undergraduate education in a physics school. Research positions tend to be described as positions In astrophysics rather than in astronomy. An astrophysicist is more interested in explaining the object and processes under study rather than the observation in its own right. Observatories that undertake routing studies of the leavens are more likely to describe their staff as astronomers rather than astrophysicists. Old established institutions such as the Royal Observatory, Greenwich, England continue to call their staff astronomers.
In terms of observation astronomy is the senior profession. The International Astronomical Union is the body responsible for naming and classifying stars, planets and other bodies found in the heavens. The search for, and classifying celestial bodies is very much the work of astronomers. Their current work involves the systematic search for near-Earth asteroids which are potentially on collision course, the search for dwarf planets within the solar system outside the orbit of Neptune, and the search for planets outside the Solar System. Astrophysicists are often through of as being involved in much more esoteric subjects such as the structure and composition of stars and galaxies.
To all intents and purposes there is little difference between astronomy and astrophysics. The difference is largely historical and pedantic. Many professionals study astrophysics but practice as an astronomer.