The following is the difference between these two words:
Habit is sometimes one’s settled practice, especially something that cannot be easily given up.
The habit of smoking cannot be easily given up.
He is in habit of getting up late.
Habit-forming drugs should be scrupulously avoided.
Do not let yourself get into bad habits.
Habit is second nature
Custom is the usual and generally accepted behaviour among members of a social group either small or large (a nation).
Custom requires us to stand when the national anthem is played.
Do not be a slave to custom.
It has become the custom for rich families to visit the health resorts in summer season.
Social customs vary in different countries.
Custom also means regular support given to a tradesman by those who buy his goods. We should very much like to have your custom means we would like you to buy our goods. I shall withdraw my custom from that shop means