The Greeks created the idea of the above gods and goddesses. They named their deity's after emotions or forces of nature. For example, Zeus was the god of lightning and thunder, things that may have seemed unexplainable at the time. The Romans adopted these beliefs, their version of the gods however, was based on things. For example, Jupiter is the supreme god, and protector of the state and it's laws.
The system of worship is also quite different, in Greece, anyone was allowed to go to the temple at anytime to worship on their own with the help of priests and priestesses. In Rome however, you brought your needs to the priest or priestess and they would pray to the god or goddess on your behalf.
One major difference between the Greeks and Romans was that while the Greeks had genders and personalities for each deity, Roman gods were left to the individual's imagination. There was no set gender or appearance for each god or goddess.