Nux Tubeman-OD Mini

If you're not playing through a real tube amp, cranked for overdrive, it's difficult to get genuine tube overdrive sound.
The original Tube Screamer pedals used an OP-AMP system, a basic circuitry that became popular for its “perfect amp” attributes. It had no distortion so it had to be overdriven or distorted by re-shaping the signal until it distorts (diode-clipping). Clipping it a little bit gives you Overdrive. Clipping it a lot gives you Distortion.