Do gains and losses across multiple different investments get netted at tax time? Or is the income tax applied individually for each?

If I make $500 in X, and -$300 in Y on the year do I owe that income tax as net $200? Or just on $500?

200 USD, assuming that you are talking about US taxes. See https://www.investopedia.com/articles/investing/062713/capital-losses-and-tax.asp (mirror):

Any loss can be netted against any capital gain realized in the same tax year, but only $3,000 of capital loss can be deducted against earned or other types of income in the year. Remaining capital losses can then be deducted in future years up to $3,000 a year, or a capital gain can be used to offset the remaining carry-forward amount.