The meaning is the same, but the verb "seek" is quite formal and old-fashioned. There are certain written contexts where "seek" might be appropriate, but you will probably never need to use it. My advice to you would be to always use "look for" in everyday contexts - for example, here on italki, you'd say that you're looking for a language partner, or you would go into a shop and tell the shop assistant what you are looking for. Don't worry about trying to use "seek" - we don't often write it and we very rarely use it in conversation.

Hi Ramin, Seeking means trying to find something this is mostly used for things that are not physical object or tangible. For example: He got fired from his job and now he actively seeking for a new job. If you are not feeling well you should seek doctor's advice. Whereas looking for a phrasal verb and it means you hope to get something that you need or want. For example: He was looking for a perfect time to break the good news to his friends. The police are looking for more evidences. Hope this helps.

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Thank you for the answers

They're synonyms