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Yea even though both of them are multiples,there is a big difference in the two:
For example if you look at EV/EBITDA multiple, for both methods though EBITDA is same but there is a difference in the way you come up with EV, for market multiple the MarketCap is based on the publicly traded share price but in Transaction multiple its the based on PRICE PAID FOR Equity, and similarly for the Market multiple the Debt is interest bearing debt but for the Transaction multiple it is the Debt Assumed.....
so on the face of it, they look similar but they are not. Moreover for the market multiples comps have to be as close as possible in terms of there business to the company being analyzed but for the transaction they have more emphasis on the size of the deal (though still industry is some what important)....
Hope i am correct and it helps you....
Biggest difference is that transaction comps will reflect the acquisition premium, which historically has been 30% or so. A standalone company is rarely valued higher than a company is acquired for, due to the value of control.
why don't the multiples from public comps account for control premiums or synergies?
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