Earnings and profits are often used interchangeably. Others might make a distinction between the two words.
In the case of earnings per share, earnings means a corporation's net income after income tax expense. However, in another context the word earnings could mean an amount that is prior to income tax expense. Some people might use the word earnings to mean an amount before all expenses are considered.
Some people use the word profits to mean net income before income tax expense, while others use the word profits to mean net income after income tax expense. The term gross profit means sales minus the cost of goods sold.
Knowing that people might use terms differently, you may need to ask the person a question to clarify their intended meaning.