You can say "I appreciate it" to anyone. It usually indicates a deeper level of gratitude than just saying "thank you." In fact, the two phrases are often used together when someone has done a big favor for you.
For example, you're behind schedule and when you're finally ready to leave for work, you discover your car has a flat tire. If you take the time to change it, you'll be late for work. Your mom steps out of the house and hands you the keys to her car. You take them and tell her, "Thanks very much, I really appreciate this!"
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