Can you identify some sources of short-, medium-, and long-term
international financing and the costs associated with each of the
sources?  How is it that these costs are different from domestic
financing sources?

Very briefly:  foreign banks or other creditors.  If a US borrower is
willing to accept the exchange risk of having debt in a currency that
may increase in value relative the dollar in which he does business
and will have to exchange to repay the debt, he may take advantage of
the lower interest rate for the foreign currency.  These result from
the overall interest rates prevailing for that currency:  depositors
receive lower interest rates and thus the banks can lend at a lower
rates with the same margin.  This might be the case in a country that
had a low rate of inflation.  In a country with a higher rate of
inflation, interest rates will normally also be higher because the
lender needs compensation for the fact that when the debt is repaid,
the value of a fixed amount will be worth less, he will be able to buy
less with it.
If this situation exists  - inflation in the borrower's country - 
there is a greater chance that the exchange rate between the two
currencies will move against him, resulting in his having to use more
dollars to buy the currency to repay his debt in the other currency.
That is his exchange risk.
It works the other way, of course, you can take the risk of putting
some savings in a currency that pays a high interest rate, but maybe
it will be devalued and you only receive 80% back in dollars.