Do I need to file a separate extension for my business?
Possibly. It depends upon the classification of your business.
If you're a sole proprietor or single-member LLC, your business income and expenses are reported on your personal (individual) tax return, which means that filing a Form 4868 also extends the business portion of your return.
On the other hand, if you need to file an extension for a corporation, S corporation, partnership, trust, or estate, you'll need to file a separate extension form (Form 7004) because the income and expenses for those entities are reported and filed separately from your personal tax return.