I recall reading about Vesta, and I believe that, like Mars and Saturn, she was more important to the Roman pantheon than the Greek. I'd like to know what the differences were between Vesta and Hestia.
Inspired by What differences were there in Greek soldiers worship of Ares and Roman soldiers worship of Mars?
The Romans worshipped the same goddess, or rather the same ideas embodied in her, under the name of Vesta, which is in reality identical with Hestia; but as the Roman worship of Vesta differed in several points from that of Hestia in Greece.
None. Both state that each is from Cronos/Saturn
Pseudo-Apollodorus, Bibliotheca 1. 4 - 7 (trans. Aldrich) (Greek mythographer C2nd A.D.) :
""He [Kronos (Cronus)] then married his sister Rhea. Because both Ge (Gaea, Earth) and Ouranos (Uranus, Heaven) had given him prophetic warning that his rule would be overthrown by a son of his own, he took to swallowing his children at birth. He swallowed his first-born daughter Hestia[.]Pseudo-Hyginus, Preface (trans. Grant) (Roman mythographer C2nd A.D.) :
"To Kronos (Cronus) and Rhea, we are told, were born Hestia, Demeter, and Hera, and Zeus, Poseidon, and Haides."
Of Priapus
PRIAPOS (Priapus) was the god of vegetable gardens. He was also a protector of beehives, flocks and vineyards.
There is no greek source of Priapus trying to rape her
Ovid, Fasti 6. 319 ff (trans.Boyle) (Roman poetry C1st B.C. to C1st A.D.) :
"Should I omit or recount your shame, red Priapus? It is a very playful, tiny tale. Coroneted Cybele [Rhea], with her crow of turrets, invites the eternal gods to her feast... Vesta [Hestia] lies down and takes a quiet, carefree nap, just as she was, her head pillowed by turf. But the red saviour of gardens [Priapos] prowls for Nymphai and goddesses, and wanders back and forth. He spots Vesta. It's unclear if he thought she was a Nympha or knew it was Vesta. He claims ignorance. He conceives a vile hope and tires to steal upon her, walking on tiptoe, as his heart flutters.
Cicero, De Natura Deorum 2. 27 (trans. Rackham) (Roman rhetorician C1st B.C.) :
"The goddess whom they call Hestia. Her power extends over altars and hearths, and therefore all prayers and all sacrifices end with this goddess, because she is the guardian of the innermost things."Orphic Hymn 84 to Hestia (trans. Taylor) (Greek hymns C3rd B.C. to 2nd A.D.) :"Hestia . . . who dwellest amidst great fire's eternal flame; in sacred rites these ministers are thine, mystics much blessed, holy and divine. In thee the Gods have fixed their dwelling place, strong, stable basis of the mortal race."
Pausanias, Description of Greece 2. 35. 1 :
"[At Hermione in Argolis :] Passing into the sanctuary of Hestia, we see no image, but only an altar, and they sacrifice to Hestia upon it."
They agree that Hestia is in charge of the hearth, but it seems that Romans believed that altars were in Vesta's territory, while the icon of Hestia was an altar.
Overall,
