Tax identifiers trip up new business owners constantly. Here's the clean version.
TIN is the umbrella
A Taxpayer Identification Number (TIN) is any number the IRS uses to identify a taxpayer - your SSN is a TIN, and so is an EIN.
EIN is for businesses
An Employer Identification Number (EIN) is a TIN issued specifically to a business. If you have employees, form an LLC or corporation, or open a business bank or merchant account, you'll need one.
The takeaway
Every EIN is a TIN; not every TIN is an EIN. Get an EIN early - it's free from the IRS and required for most of the steps that make you a real business.