"30-06" and "30-06 Springfield" are the same thing.
It is named the 30-06 Springfield because:
-it shoots a 30 caliber bullet
-the "06" is the year it was commercialized (1906)
-Springfield is the company who created it
The cartridge has its roots in the Springfield 1903 military rifle.
They made some changes to the cartridge, I believe they elongated the neck, and then commercialized it in 1906 as the 30-06 Springfield.
Cartridge names can be mighty confusing, but generally the names give the bullet diameter and the creator or some way to distinguish itself from other cartridges with the same bullet diameter.
For example the 308Win is a 30 caliber bullet and Winchester created it.
Remington created the 270 Rem (which has a 0.277" diameter bullet).
A cartidge such as the 30-30Win has a 30 caliber bullet and was created by Winchester. The "-30" comes from the fact that the case holds 30 grains of water.
The 7mm-08 Rem ("seven-millimeter-oh-eight" not "seven-millimeter-aught-eight") is a 7mm diameter (.284") bullet and gets its name from it's parent cartridge, the 308 Win.
The 22-250 has a 22 caliber bullet and the case was derived from the 250-3000 Savage. The 250-3000 Savage got it's name because it's 25 caliber, designed by Savage, and could push a bullet 3000 fps.
Confusing isn't it?