Is the word transmission and trans-axle the same?

Yes and no. Hard to think of good answer but Trans-axle is where you have the transmission and axle drive unit built into one. Front wheel drive. But you can have a transmissione do both front and also supply power to rear axle, AWD(All Well Drive). 2000 is where everything starts to change, in some vehicles other then P/U trucks still use a regular trans and a transfer case to direct power to the front axle.