Is the language option on the form the same that appears on the conditions?

Small question:  what does the "language" field refer to in the Conditions box?

Is it to the language chosen by the user when he starts to fill in the form ? (Represented by the small flag at the top of the form).

Yes, the conditions can also be triggered based on the selected language, that will help to change the thank you page or the email template based on the selected language. 

Here are some guides that will help you using conditions based on the language: 

https://www.jotform.com/help/334-How-to-Change-Email-Template-Sent-Based-on-the-Language-Used

https://www.jotform.com/help/333-How-to-Change-Thank-You-Message-Depending-on-the-Language-Used

I hope this helps.