Does the July 15 extension apply to other types of tax payments?

The extension to July 15 for filing and paying federal and state income taxes only applies to income taxes.  As of the writing of this answer, this extension does not apply to filing and paying payroll taxes, making installment agreement payments, making Offers in Compromise payments and other similar payment obligations.  The deadlines for returns and payments for any other kind of tax is still the normal filing date for that tax. However, the automatic extension does apply to estimated tax payments for 2020 due on April 15, since that is a tax on income.  Your first estimated tax payment will be due July 15.

For South Carolina, the filing and paying of income taxes is extended to July 15.  The deadline for all other taxes, such as payroll taxes, sales tax, unemployment taxes, etc. has been extended to June 1, for all taxes and returns due on or after April 1.