A lamp dimmer controlled iron uses a phase controller which doesn't have any feedback so adjusting the control just alters the voltage delivered to the element.
A thermostatically controlled iron has a temperature sensor inside the element so if it's too cold, the element turns on, if it's too hot, it turns off.
A thermostatically controlled iron is always better because the temperature is regulated so the control won't need adjusting when soldering large connections which require more heat energy.
Is this the soldering iron you bought?
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If the answer is yes, it's a cheap phase controlled iron, not a proper thermostatically controlled iron. You could have saved yourself some money by buying a 50W iron and connecting it to a lamp dimmer. I have one of these irons and it's not too bad but I did feel a bit ripped off.