The issue is difficult, but can be useful to clarify that there were no "stable" terminology in ancient Greece science.
Eudoxus of Cnidus's (scholar of Plato : 408–355 BC) lost astronomical works were titled : Phaenomena (Φαινόμενα) and Entropon (Ἔντροπον).
The lost book of Aristotle's pupils, Eudemus of Rhodes (c.370 BC - c.300 BC): History of Astronomy (Άστρολογικὴ ἱστορία), is clearly influenced by Aristotle terminology.
We can list also the didactic poem Φαινόμενα ("Appearances"), Aratus (c.315 BC – 240 BC) and the only preserved work of the great astronomer Hipparchus (c.190 – c.120 BC): Τῶν Ἀράτου καὶ Εὐδόξου φαινομένων ἐξήγησις ("Commentary on the Phaenomena of Eudoxus and Aratus").
Theodosius of Bithynia (c.160 BC – c.100 BC) wrote the Sphaerics (Σφαιρικά).
Geminus of Rhodes (1st century BC) only surving work is Introduction to the Phenomena (Εἰσαγωγὴ εἰς τὰ Φαινόμενα).
Claudius Ptolemy (c.AD 100 – c.170) main works are :
the astronomical treatise now known as the Almagest, although it was originally entitled the "Mathematical Treatise" (Μαθηματικὴ Σύνταξις) and then known as the "Great Treatise" (Ἡ Μεγάλη Σύνταξις)
the astrological treatise sometimes known as the Apotelesmatika (Ἀποτελεσματικά) but more commonly known as the Tetrabiblos (Τετράβιβλος) meaning "Four Books" or by the Latin Quadripartitum.
In conclusion, during six centuries of Greek astronomy, we have very few tratises with Astronomy (or Astrology) in the title.
Thus, my personal suggestion is do not read too much about a definite disciplinary separation in ancient science.
More specificaly, about Plato and Aristotle, see :
Plato, Rep., VII, 528E-on :
Astronomy (astronomìa) will accordingly be fourth in order, and Stereometry third. [...] as studied at present [Socrates replies], Astronomy turn the soul's eye down, though the bodily eyes looks upward. True astronomy is not observation of the visible heavens [...]; it is a mathematical science, which studies the true movements of intelligible stars and uses the visible firmament as its orrery. We shall therefore pursue Astronomy by making use of problems and leave the heavens alone.
Aristotle, Met, B, 997a34-on :
And astronomy (astrologìa) also cannot be dealing with perceptible magnitudes nor with this heaven above us. [...] nor are the movements and complex orbits in the heavens like those of which astronomy talks. [The context is a critique of Plato's theory of Forms.]
We can speculate about what are the different points of view discussed here, but it seems quite clear that it is not the difference between :
Note see :