My topic is money, budgeting and public finance(s?).
Do you say public finance or public finances? (like in http://news.bbc.co.uk/1/hi/business/8573128.stm)
Budget has two sides, spending and receipts? Why is one singular and second plural?
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In response to your first question, I believe that finances (plural) have to do with the funds of the government (i.e. the little gold we have left int the Treasury), whereas public finance is the management of those funds.
If you type in "define: finance" on google, you get:
Finance is the science of funds management.
whereas if you perform the same search on "finances", it outputs:
funds: assets in the form of money
In response to your second question (spending vs. receipts, plurality), see the wikipedia page on classification of nouns. One could be considered non-concrete and one concrete, or perhaps one is uncountable and the other countable.
Hope that helps!