When saying goodbye, take it easy and take care are virtual equivalents. I wouldn't construe either one to mean anything more than a polite yet standard way of saying goodbye when two people depart from each other.
I also would like to know what situations I can use the phrase "Take it easy."
There are several uses of that phrase besides the standard goodbye. In context, it can be used when:
- you try to calm someone down (Bob was about to get in a fight when his friends told him, "Calm down, take it easy.")
- you want someone to be cautious (Jill was teaching her daughter how to drive, when they approached a sharp turn in the road. "This road takes a sharp turn up here," Jill said. "Take it easy on this curve.")
- you want to tell someone they should embrace a more carefree lifestyle (Ted said to his friend Janet, "You stress out too much; you should just learn to take it easy.")
- you want to help soothe or calm someone's anxieties or emotions (Brenda broke down in tears when she told her husband the bad news: she had just lost her job. Her husband embraced her, and tried to offer some reassurance. "Take it easy, honey," he said. "Maybe this will work out for the best somehow.")
Similarly, "take care" is usually just a shortened form of "take care of yourself," which is why some folks may say that to you when you're not feeling well, either physically or emotionally.
Both phrases often have undertones of empathy, although "take it easy," usually means to slow down or relax, while "take care" means to get well, or remain in good health or spirits. As I said before, though, when either of these are used as a substitute for goodbye, there's a good chance the speaker used one instead of the other only arbitrarily, unless something earlier conversation might have changed that.
It's probably worth noting straight away that "to get" is increasingly common in OP's context. As this link shows, X got me interested in Y was virtually unknown a century ago, but it's now far more common than made me interested in.
But there are subtle syntactic and semantic differences. As noted above, of OP's first pair...
1: This book got me interested in Buddhism.
2: This book made me interested in Buddhism.
...#1 is more common, but both are acceptable. And so far as I'm concerned, they mean the same. But...
3: This book got me thinking about my future
4: This book made me think about my future
5: ✲This book made me thinking about my future (where ✲ marks a usage as unacceptable)
...with OP's second pair we can't just replace got with made. Notice also that we can explicitly use the "marked infinitive" (to think) with got (also to [present participle], but I don't know what to call that)...
6: This book got me to think about my future
7: ✲This book made me to think about my future
8: ?This book got me to thinking about my future (perhaps not everyone would accept this form)
9: ✲This book made me to thinking about my future
On the basic of the above, I suggest it's well worth learners spending some time becoming familiar with the syntactic possibilities of to get. Because it's increasingly common in modern speech, and can probably be used in more contexts than to make, it's likely to be more useful over the long term.
On the semantic front, note that to make often carries implications of deliberate and/or forceful actions. Thus with this pair...
10: He got me to eat snails in garlic butter
11: He made me eat snails in garlic butter
...there's a much stronger implication that in #10 he persuaded me (possibly quite easily). It would be quite reasonable for the utterance to continue with "...which I really enjoyed". But #11 implies he forced me (much against my will). That one might continue with "...which made me feel really queasy".
Best Answer
This is the difference between "active" and "passive" verbs.
An active verb is when the subject does something. This is the more common form, and probably what you are used to as the "normal" form.
A passive verb is when the subject is the target of the action. Usually we indicate a passive with "is" or "was" plus a past participle of the verb.
For example:
Active: Al gave the box to Bob.
Al is the subject. Al did the giving.
Passive: Al was given the box by Bob.
Al is the subject, but Al is not doing the giving, he is doing the receiving.
Sometimes people use "got" rather than "is/are". We could debate whether this is grammatically wrong, but it's surely informal.
So more formal: Al was fired by his boss.
Informal: Al got fired by his boss.
If we said, "Al fired Bob", that would mean that Al was doing the firing, and Bob was the person who was fired. "Al was fired by Bob" or "Al got fired by Bob" means Bob was doing the firing and Al was the person who was fired.
So to get to your example: Blushing is something that you do, not something that is done to you. So the correct phrasing is, "I blushed when she looked at me."
You might Google/Bing "passive verbs" for more information.