Is the 6,5-06 the same cartridge as the 6,5-06 A-square?

No, the standard 6.5x06 has a 17 degree shoulder, the A-Square a 34 degree shoulder and the improved a 40 degree shoulder.

Now for the best news, the standard resized cartridge will fit in an A-Square cut chamber but the A-Square fireformed cartridge will not fit in a standard chamber.... Several suppliers offer the 6.5x06 standard and improved as regular priced dies.

So you can size 270 brass with a standard 6.5x06 sizing die, trim and fire form, then neck size and deprime with a 6.5x06 improved sizing die. Thus no expensive A-Square custom dies. If that is where you were going with the question.
Ed