The Joule thief has a 1.5V battery and has an output power of about only 0.0075W. It uses a low voltage, low current little transistor.
Your ultrasonic bath circuit uses a 323V supply (the 230V mains rectified) and has an output power of maybe 7.5W or more.
Its 2SC3688 big power transistor is used to make the horizontal deflection and high voltage in a colour TV and is rated at 1500V, 10A and switches very fast.
Your transformer probably has a ferrite core, has very low capacitance and is probably a voltage step-UP type.
Edit: The schematic of an ultrasonic cleaner circuit is in Google. It uses a high voltage, high current and high power transistor and a transformer with a ferrite core. it recifies the 120V mains to make a pulsing 169V supply. The schematic is in old text: