Both the Code 39 - Regular and the Code 39 - Full ASCII barcode symbologies contain the same 43 character set, as well as the same start and stop characters. However, Code 39 - Full ASCII uses special two-character combinations from the 43 character set to allow for the representation of all 128 ASCII characters. In other words, you can encode any of the standard (not the extended) characters from the computer's keyboard into a barcode, as well as the ASCII control characters.
Example:
Let's take a look at printing lowercase letters. No lowercase letters are native to the Code 39 character set, only capital letters. Therefore, when printing Code 39 - Full ASCII, lowercase letters are represented by generating the barcode symbol for a plus sign (+), followed immediately by the barcode symbol for the uppercase version of the letter. So, to print the letter "a", you would actually print a barcode containing "+A".
Now, suppose we scan the barcoded Code 39 - Full ASCII "a" that we printed as described in the previous paragraph. In Full ASCII mode, the barcode reader would decode the plus sign, and then, rather than transmitting it, would look at the next barcode character symbol (in this case a capital "A") and perform a Full ASCII conversion. The barcode reader would then transmit just the lowercase "a".
If the barcode reader had Full ASCII translation disabled, no translation would be performed and the actual characters "+" and "A" would be transmitted.