Whats the different between federal ID number and employer federal ID number?

Nothing. They're the same thing.

**-When I ask a employer for their Federal ID #, they say, "the EIN", I say 'yes'.

A FEIN or EIN is 9-digits.
If you're a sole proprietor your social security number can be used as your FEIN.

On the State level, your FEIN won't change and will help identify your business within different agencies .
When you file to determine if you're liable or non-liable for unemployment tax, you FEIN will be connected to your unemployment tax id.
It will also be used for withholding tax. A state withholding tax id may have a few extra characters but your FEIN should be there.
You may also need your FEIN for sales tax purposes as well.

For IRS purposes, they are the same thing.
The state may use a slightly different number for their purposes.

Individuals use an SSN.
Employers use an EIN.
Estates/trusts use an EIN.
Aliens use an ITIN when they aren't eligible for an SSN.

Collectively these are all called TIN (taxpayer identification number).

Basically the same thing. You federal id number is your social security number. EIN is the 9 digit number that companies use

Since companies pay taxes just as an individual does they are given a number for records such as W-2's and other tax related filings. Your social security number is your federal ID number. Generally you will find both of these on documents regarding tax issues.