It depends on the context! They can be quite different, eg:
After leaving the Army he made his living as a taxi driver.
He lived on bread and cheese for two months.

What contexts do you have in mind?

I was thinking about the general meaning. But I'm aware of the fact that without any context it's always quite difficult to translate. But thanks anyway

there are similarities, but the two don't mean the exact same thing. For instance:
Earning $250,000 a year, John makes a good living for himself and his family.
John and his family have $250,000 to live on per year; that's not bad.

Wie du es schon sagst: seinen Lebensunterhalt mit etwas verdienen vs. von etwas leben.

"make a living from/by" steht normalerweise mit einer Taetigkeit. "Lives on" steht normalerweise mit einem Substantiv, dass die Einkuenfte oder deren Herkunft beschreibt.

John makes a living from renting his mother's old house.
John lives on the rent he receives for his mother's old house.

Betty lives on welfare, Claus on income from stock options. Both make a living from profiting from other people's work. ;)