Cultivate and Grow

Cultivate

Cultivate most commonly means to prepare the soil for growing plants of some kind. It involves loosening or breaking up the soil. On large farms, that is done by using a machine called a cultivator.
By cultivating the soil, the roots of the plants can absorb water and nutrients. It also removes weeds that can interfere with the plants' growth.
Nowadays farmers are more aware of environmental issues. They try to use ecological materials that are easy to cultivate and that can tolerate any soil.
Cultivate also means to improve or develop something, like a talent, by training. For instance, a singer can cultivate her voice. People can also cultivate a new interest or hobby, or they can cultivate a friendship.
It's never too late to cultivate a new interest. Last year, Bob's grandmother started taking flying lessons, and just last week completed her first solo flight.
When Ree got a new teaching job in another state, she had to cultivate new friendships among her colleagues. She found that she had a lot in common with several of them.

Grow

To grow is to increase in size through the use of some type of food source. Plants on a farm grow by absorbing nutrients from the soil or fertilizer that has been spread on them. To grow can also mean to increase or expand.
If my brother grows any more, my parents will need to buy him a new bed. His big feet already hang over the end of the bed he has now.
When Mark Zuckerberg created Facebook while still in college, he never imagined that it would grow to its current size.
A figurative use of grow is to say that a thing or person has grown on you, which means that, over time, you have come to like it. When someone is always busy or on the move, you can say they don't let any grass grow under their feet.
Jeanette didn't like her new hair color at first. After a couple of days and compliments from her friends, the new color grew on her.
No grass grows under Edward's feet. From the time he gets up in the morning until he goes to bed at night, he is on the move, rushing from one activity to the next.