It might vary depending on the language used by the casino. In most cases, there is a slight difference, especially in the way the bonus is obtained. Free spins can be a no deposit offer where extra spins are an ‘extra’ added to your deposit bonus offer. These are generally added to a deposit match bonus.
Some casinos might trail off completely and refer to your no deposit spins as bonus spins. While the name changes, the offer remains the same. The important thing remains, to read the terms and conditions to be sure of what offer you will receive and what they expect from you.