From memory I think AES and SPDIF are pretty much identical in terms of data. There were differences in the electrical signal levels (balanced vs unbalanced) and SCMS.
S/PDIF was simply a lower voltage consumer format standard of AES (which can be balanced or unbalanced)
as gordon mentions, SCMS is part of the 8 'subcode' bits and is basically S/PDIFs attempt to cripple copying in the consumer standard. There is some other random useless (for our purposes) ASCII-codable info transmitted in the subcode
while they are unique, for our purposes there seems to be no difference, ive used basic xlr3 to coax cables to clone dats for 25 years. i can put a meter on it but im pretty sure it just lifts the 'cold' lead of the balanced connector, similar to analog balanced > unbalanced cables. im guessing the signal level in such a case would also be dropped on a digital cable going from balanced to single-ended. AES is technically up to 7V while spdif is 0.5V. Ive used fancy Canare impedance converters for years, but that was more of an effort to be 'technically correct', and more importantly, it provided the right connectors on each end (XLR3 to BNC) for me to connect A to B. That said, in my experience, AES to S/PDIF either works, or is digital garbage, and is almost always a 'sounds good, is good' proposition
unfortunately, none of that overly techy BS helps OP as it is almost certain his DAT deck already has a S/PDIF compliant output. More importantly, he needs to take this digital output and capture it with a soundcard or known good recorder. there are 100 ways to skin that cat. but to simplify, thats where its at.