For what it is, I'll leave the explaining to Charles Cottle, from The Hidden Reality:
There is the raw (actual)position consisting of the exact options that contribute to an overall strategy. For every raw position there are a number of alternative positions called synthetic positions (synthetics). A synthetic position has the same risk profile as its raw position and achieves the same objectives.
What that means is that the risk profile of an option strategy can be duplicated via different combinations of options and/or stocks. A few examples:
A covered call is a synthetic naked short put
A married put is a synthetic long call
A collar is a synthetic vertical spread
There are dozens of combinations that can duplicate the risk profile of different combinations.
The problem seems to be that some people feel that the positions must me identical in every respect to be synthetically equivalent. The most common objection is that of different capital/margin requirements. - that if one position needed more money to trade than the other, they can't be synthetically equivalent.
One fellow didn't feel that a long call/short corresponding put wasn't synthetically equivalent to long stock, because he could get the option combo on margin, whereas the stock required the full investment of the value of the stock. That *may* be true for some traders. But it is certainly not true for others due to different margin rules, haircuts or whatever.
The logical extrapolation of that logic would be that stock bought on margin is not the same as stock bought for cash.
In any case, capital/margin requirements are not relevant to synthetic equivalence. What is relevant, it the risk profile... the payoff diagram adjusted for cost of carry and dividends if necessary.
Capital/Margin is not considered when looking at synthetic equivalence.