Yes. Technically, they simply refer to the type of state law under which the entity was formed. In some states such as California, an organization would be formed as a “non-profit corporation,” whereas in New York it would be formed as a “not-for-profit corporation.”
Many people ascribe different meanings to the terms, but do so mistakenly. Indeed, the term “non-profit” is less descriptive than “not-for-profit,” yet it is used much more commonly. The Law Firm for Non-Profits naturally prefers the term “non-profit.”