Some ways of saying thanks, in order of "strength".

Thanks!
Thank you!
Thanks a lot!
Thank you very much!
Thank you so much!
Thanks a million (informal)
Thank you, that was really helpful! (OR that really helped me)
Thank you, I really appreciate it! (I am really grateful).
Thank you, you are so kind!
Thank you, I can't tell you how grateful I am!

It sounds a bit more serious and like you *really* mean it if you say "thank you" instead of "thanks". Just a minor nuance.

Here is my experience of the "thank you" phenomenon in English, ignore it at your peril!

In English (UK) it is EXTREMELY important to say thank you A LOT!
As soon as there is the slightest reason to thank someone, you must do it.

If you buy something in a shop, you might end up saying "thank you" three times as you pay, recieve the change back and perhaps they help with something like packing the goods.

As soon as you receive anything at all, you must say "thank you".

If you don't, people think you are a bit rude/cold.

English people do not realise that this is quite unique for the English language. Even though they are quite tolerant to mistakes by foreigners speaking English, this is something that they don't understand. They just think that you are a rude person if you don't say "Please" and "Thank You" all the time.

This is a difference between my language and English, so I had to make a huge effort to start this enormous "thank you" thing when I moved to England. I know that people in Russian speaking countries don't use "thank you" a great deal either. Not because they are rude, or because people don't help each other but it's a different way of speaking and behaving.
Russian people actually seem rude to English speakers because of this.

If you read an English speaking guide to Russia etc, it's full of advice about how not to be offended when people are "rude" etc. In reality, (at least in Ukraine and Belarus) people are both kind and helpful in most cases The customer service is not exactly fantastic in some places but it is not anywhere near as bad as the English speaking guide books make out. Sometimes you get much better help than any English person would bother giving. It's all due to misunderstandings on the part of the English people - language difficulties and a different attitude to when it is necessary to say "thanks" and when it is not

So if you are Russian and read this:
Be very careful to say Thank you when you speak English - a lot more than you normally would! As soon as anyone does anything at all to help you, or give you something. Even if it is their job etc.

If your English speaking boss sends you an email ending with "Thanks!" it's a way of saying "Thank you for doing what I say right away! (implicitly, do it now!)
Do not end emails with "Thanks!" to customers or people who are senior to you, it makes you sound a bit disrespectful.
Many foreigners make this mistake that's why I warn about it.