Romans had little mythology of their own before they conquered Greece. The Greeks brought their Greek heritage with them and the Romans used captured Greek scholars to tutor their children. Overtime, the Romans reinterpreted their mythology to mirror the ancient Greek mythology which led to their existing Gods getting many of the characteristics of the Ancient greek ones.
Keep in mind that not all Roman gods are similar to Greek gods, for example, Saturn, Quirinus and many others were worshipped the Greek gods were introduced. Romans also have gods from other cultures too.
The Greek mythology and the romans mythology have some things in common. Most importantly, the Romans obtained vigorously from the Greek pantheon. The Greek gods are the same as the Roman gods just with various names as far as their philosophy.
Many, if not every, Roman legend concentrated more on morality and governmental issues. The account of Romulus and Remus is a major contrast, also the way that Romans consolidated outside religions (Vedic religion, and so forth.) and other ideologies into their convictions.
Then again, the Greeks had made their own gods and were interested more with nature and cosmogony than the Romans. In any case, heroism is a topic which is similar to the two myth.