Begin and start are almost the same, but there is a small difference between this two words.
If you like to sound formal english language Begin is more common in that case.
Example
He started / began to play game to hours ago.
We will begin / start dinner at 7.
It is time to begin / start project for school.
Start something like a journey or we can start a vehicle ( engine, machine ). In this cases we never use Begin.
Example
We started a day with good coffee.
My wife show me how to start a electric car ?
At last the car started.
