What is the difference between Julius Caesar and Augustus/Octavian Caesar?

Julius Caesar was a roman general and statesman who started a civil war.  He's the one who had an affair with Cleopatra, and fathered a child with her.   He wasn't really rivals with Mark Antony.  Antony was his military subordinate, friend, and political ally.  Antony only began a relationship with Cleopatra after Caesar was assassinated. 

Octavian was Caesar's grand nephew.  He was the son of Atia, the daughter of Julius Caesar's sister.  In 44 BC, Julius Caesar, who had named himself Dictator after defeating an opposing faction in a civil war, was assassinated by a group of traditionalist Senators who were trying to preserve the Republic.  In Caesar's will he named Octavian as his adoptive son and left him his fortune and family name, which made the still teenage Octavian an overnight power player in Rome.  Over the next two decades, Octavian became a general and statesman, at first allied with Caesar's old friend Mark Antony and then opposed to him.  After Octavian defeated Antony in another civil war (prompting the famous double suicide of Antony and Cleopatra), Octavian ended up having himself declared Emperor, a new position, effectively ending the Roman Republic.  For his regnal name, Octavian chose the name Caesar Augustus. 

Their differences were more important. Caesar was a great (according to his writings) general but had little patience for administration and had a bit of an ego. Augustus surrounded himself with able men. ... Caesar set himself up as dictator of Rome and flaunted his power.

Gaius Julius Caesar had an affair with Cleopatara VII Philopator, next to last  pharaoh of Egypt. They had  a son Caesarion. Caesar was more a military rival with Marc Anthony than a love rival.  Julius Caesar was elected Dictator for life and was the great uncle of Octavian who he named as his heir. Octavain became the first Roman Emperor. Romans changed their names often. Augustus was born as Gaius Octavius, after his defeat of Marc Anthony he had the Senate change his name to Imperator Caesar divi filius Augustus.

Julius Caesar came 1st living (100BC-44BC) he was the military/ political genius. He became the popular dictator of the whole Roman empire making much historical progress.

Octavian was Caesar's grand nephew the grandson of Caesar's sister. He came last in time  living (63BC-14AD). Since Caesar when he was killed (44BC) left no clear heir Octavian claiming to be a relative fought a long civil war to takeover as new dictator of the empire, won, and in fact became 1st emperor as 'Augustus'.

It was Caesar who had the affair with Cleopatra (48BC-44BC) hosted her in Rome and had a son by her 'Caesarion' (his true heir by birth). Caesar's affair with Cleopatra, having a blood heir with her and ditching his wife (who he disliked) is largely what got him assassinated in 44BC.

It was Caesar who had Marc Anthony as one of his top generals and Marc Anthony who thought he should take over after Caesar or at least Caesar's true son Caesarion should. He joined forces with Cleopatra (43BC) became her lover and together they fought the long 13 year war against Octavian till (30BC).

In 30BC 14 years after Caesar's death Octavian won all, killing everyone else...Marc Anthony/ Cleopatra/ and 17 year old Caesarion, etc. and took over rulership of the whole Roman world as Augustus Caesar (his majesty Caesar), he put in 'Caesar' as a family name to remind everyone he was Caesar's grand nephew.

WE DON'T NEED TO EXPLAIN IT WHEN YOU CAN EASILY READ ABOUT BOTH MEN ON WIKIPEDIA, LAZYBONES.