As mentioned in the comments, the products depends on various factors like nitrating agent, concentration etc. If you use dilute nitric acid, you will get a mixture of mononitrophenol but when you use concentrated nitric acid, you will get picric acid. Note that although picric acid is the targeted product, you will get all sorts of dinitro- and mononitro- isomers as well. To get pure picric acid, steps are taken to distill of the DNPs and MNPs or make the reaction more selective. So, 2,6-dinitrophenol is also a product of the reaction. It's just that it's too minor of a product to mention.
Side information:
Pure 2,6-DNP can be prepared by separate sulfonation and nitration of o-nitrophenol. It is also a byproduct in the synthesis of 2,4-DNP (2,4-Dinitrochlorophenol is heated with 6% aq. $\ce{NaOH}$ at 95-100 °C for 4 hours which hydrolyzes it. 2,4-DNP is the product and is precipitated by adding acid and is filter off. The solution contains the more soluble 2,6-DNP which is separated by adding excess of acid).
Source: Toxicological Profile for Dinitrophenols, U.S. Department of Health and Human Services, 1993