We are known that there are two transformer circuits in electrical distribution. One are power circuit & second are control circuit. The transformer who connected HT bus bar and supply feeds to HT motor is all most Power transformer because it is connected with power circuit. Other low voltage transformer is mostly connected in control circuits. It's distributed power (voltage or current) to any machine so it called distribution transformer.
A power transformer is a transformer which will be feeding smaller transformers in the electrical network connected to it. The smaller transformers which feed the actual load connected to it such as motors, lighting, heaters etc are called distribution transformer.
The major difference is in the construction of the transformer. The oil present in the transformer will expand as the load rises thus raising the oil pressure in the transformer tank. The range of the pressure which a transformer can with stand will be a major factor for power transformers. Hence the power transformers will have a heavier tank construction to avoid accidents in heavy and over loaded condition.
General present in substations. The monitoring, protection and preventive maintenance for this is of high importance. Any voltage level can be manufactured but with higher capacity i.e. above 1.5 MVA (as per transformer industry) power transformers are designed to be more efficient when compared to distribution transformers.
Distribution transformer is not as efficient as power transformer. The size and the load in the transformer will not be steady. And will not have any protection such a power transformers. These transformers will be placed in the nearby locality from which we get power. The secondary side will always be LV i.e. 415 volt.
Distribution transformers step down from HV (11 or 33 KV) to 433 or 250 Volts & supplying LT consumers. Step up / Step down transformers from 11 KV to higher voltages are power transformers. Earlier there were 3.3 & 6.6 KV voltages in transmission voltages but now they are completely phased out & these voltages are existing in HT services for their HT motors for which the consumers order those motors specifically. As they are not in use by power utilities they are not classified. In distribution transformers the capacity can go up to 1500 KVA. To avoid transmission losses higher voltages like 400/ 500/ 700 KV are used & to contain distribution losses they use smaller transformers & higher gauge feeder lines. Transmission voltages have gone up to 700 / 1100 KV. All transformers were earlier using Transformer oils which are a mineral oil. For indoor transformers in Power houses where there is fire hazard special oil is used which is fire proof.
When it comes to functioning both work with same principle and no difference.