What is the connection between Roman and Greek mythologly?

They literally are the same thing. Greek mythology was carried over to Latium, I believe it was, by Aeneas. Eventually, the Latin people began picking up the religion. When Romulus and Remus (or really, just Romulus, since he killed Remus) founded the city of Rome, the Romans (who were mostly the Latins) followed the religion, but all the names in the religion were changed.

For instance:

Zeus -- Jupiter

Poseidon -- Neptune

Hades -- Pluto

Hestia -- Vesta

Hera -- Juno

Demeter -- Ceres

Hephaestus -- Vulcan

Hermes -- Mercury

Ares -- Mars

Aphrodite -- Venus

Athena -- Minerva

Apollo -- Apollo (no name change)

Artemis -- Diana

Dionysus -- Bracchus

The list continues, but those are your majors.

So, really, there is no big difference. Just the names and the people that worshipped them (the Greeks or the Romans)