phrase usage - Thanks vs Thank you vs Thank you so much?

What is the correct way to say "thanks" to anyone in any situation?

Does it make any difference depending on context or situation?

Answer

There are various levels of showing gratitude verbally (in order of formality)

Ta (BrE)

Thanks (AmE, BRE), Cheers (BrE)
Thank you (AmE, BrE)
Thank you very much (AmE, BrE) Many thanks (BrE)
Thank you very much indeed (BrE), Many thanks indeed (BrE)

The standard expression when something has been done for you is

Thank You (with eye contact and a smile)

it is polite and formal and can be used for any occasion.

Thanks is less formal and can be said casually
Cheers is similar to thanks and used extensively in Britain
Ta is even more colloquial and used when also saying goodbye

Look forward to seeing you again mate, ta (as he waves and walks off)

Thank you very much shows abundant gratitude as in here (song starts around (00:55)

In situations when one would say "thank you" once, like after a dinner party

Thank you very much for inviting me, I really enjoyed myself

Thank you very much for driving me to the airport
Thank you very much for your kind present

In situations where "thank you" might be used multiple times, as in a restaurant, the standard "thank you" should be used. For example, each time one's water glass is topped up. It's best not to overly use very much.

Brits may add indeed when something nice has been done for them which was not requested

P1: Excuse me, you forgot your hat
P2: Oh, thank you very much indeed

P1: I took the liberty of ordering you a cab to get home
P2: Many thanks indeed

Other expressions can be added to thank you when appropriate

Thank you from the bottom of my heart
Thank you that's very kind of you
Thank you kindly
Thank you much obliged (used in Southern AmE)

and even

Thank you, thank you, thank you!

Children in Britain are told to

Mind your P's and Q's !
Mind your pleases and thank yous

You can never go wrong saying "Thank you"