As a member of Greek Diners Club (but also and something like an insider due to my job) I can tell you that all non North America cards that have the mastercard logo on the back are accepted as mastercards in US and Canada and the majority of Internet sites. (Some local franchises haven't upgraded their systems yet and those cards have problems in the US). Elsewhere they are accepted only if the establishment has an agreement with the local Diners Club company.
If it is more clear the Americans cards have one number 55XX-XXXX-XXXX-XXXX,
while the non-Americans have two, one official (in the front) 36XX-XXXXXX-XXXX and one only for north American POS systems 55YY-YYYY-YYYY-YYYY.
As for Discover, it is kind the same as the Mastercard Diners Alliance. Discover cards will be accepted to outlets in Europe, Asia and Oceania that accept Diners Club cards without any change to card number (at least this is the initial plan).
Closing, Diners Club was (and to some point, especially to Europe and Asia, is and will be) a special product that brings and maintains upper level customers to Citibank. The bank is not seeing DC as a line of profit but as a key to a special customer audience that wants to approach and also it is the only product that directly competes AMEX Green, Gold (Personal Diners Card) and Platinum (Carte Blanche or Prestige here in Greece). Here is still an exclusive product for middle and upper class. I believe is the some in the US but the mastercard logo has lifted some of the product uniqueness.