Yes gratuity and tip are the same thing.
The word gratuity is just another word and meaning for tip.
So if you have a waiter that you want to tip you could give them a gratuity which is a tip.
In employment the tip that an employer would give is mostly called a gratuity and not a tip and when you give a waiter a tip you call it a tip.
But when you do give a waiter a tip you're giving the water a gratuity payment.
Some employers will give their best employees that have been working for them for at least 5 years a gratuity payment which could be a one lump some of money at the end of the year.