hey Saphron234.
the tarjeta de salud and tarjeta sanitaria are one and the same.
in order to get one, you need to be a contributing memeber of society (eg. working and paying taxes), retired, minor or student.
the tarjeta sanitaria comes with paying social security and that comes with having a job (working for someone else and they pay your ss for you) or having your own business in which case you pay the ss via "autonomos" (kinda like a private business person tax).
as an american without papers, you will have to get private health insurance but don't fret, it is dirt cheap here in spain compared to the u.s.a.
have a look at...
www.sanitas.es www.adeslas.es... they are the 2 most popular providers.
as for the NIE thang, am afraid it has been discussed to death here on the board. there are a TON of good threads on how to go about getting it so you will have to do your homework and search around

saludos,
jer...