There are a lot of details available about how non-discriminating monopoly and perfect competition are different. In a perfect competition market, this means that there is no company that is better than all the rest because all of the companies have no control of what is going to happen next or how the consumers are going to react. In a non-discriminating monopoly, all of the items are being sold to everyone at the same price.
The only similarity between the two is that they can provide some advantages to the people who are involved. The companies will be able to serve all of the customers well and the customers will provide their equal attention to the different companies available. It is apparent that the chances of this situation happening are not very likely especially at present time.