is there a difference between "I want to learn cooking" and "I want to learn how to cook"

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Answer

For me there's a small difference.

"I want to learn cooking" emphasizes  more all aspects of cooking. Not just the required specifics of a particular meal, dish, or particular recipe, but more depth. That is I want to learn more than *just* how to cook something. I may want to know the several ways of cooking it, the history, the variations, etc. And I want to know about cooking in general - I want to understand it almost as much as I was trying to understand any  particular area of knowledge.

"I want to learn how to cook"  *can* mean the above, but for me it generally means I have less requirements in what I want to know. I just want to know the practicalities of cooking - ie how to prepare basic meals. I'm not so interested in treating 'cooking' as something I need to go into any great depth with.

This is my take on the 2 sentences :)

Answer

"Learn to cook" is about 10x more common than "learn cooking."

Here is the Google Ngram.
https://books.google.com/ngrams/graph?content=learn+cooking%2C+learn+to+cook%2C+learn+how+to+cook&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Clearn%20cooking%3B%2Cc0%3B.t1%3B%2Clearn%20to%20cook%3B%2Cc0%3B.t1%3B%2Clearn%20how%20to%20cook%3B%2Cc0

To learn how to [infinitive].  << Standard, given by dictionaries and by English Grammar in Use (Unit 54).
To learn to [infinitive].  << Standard, reduced form, most common 
To learn [gerund].  << Nonstandard
To learn [noun].  << Standard

Examples:
To learn how to play the piano.
To learn to play the piano.
To learn playing the piano.  << Nonstandard.

"To learn cooking" may be an exception.  Google Ngrams show meaningful usage.
To learn Italian cuisine. 
To learn Italian cooking. 
To learn cooking. <

Answer

different in what way. They both mean basically the same thing.