A wide gap due to tongue thrust. Is buying the retainer online give the same result as the one the dentist prescribe? (Photo)

The one photo reveals multiple issues.  In addition to the gap you have flairing of the teeth, a narrow maxilla and probably a compromisd airway.I suggest you work with an Oral Myofunctional therapist to learn exercises to retrain your tongue.  Some patients see resolution just from that.Ideally, I would suggest expansion with a DNA Appliance to correct narrow maxilla, give more posterior room for your tongue and improve  your airway.  Tongue thrusts are frequently a clue to evaluate the airway.