Each of those is a PC-Card (aka PCMCIA) & would work in a laptop with a PC-Card slot.
PCMCIA is the original specification & uses a 5V/16 bit interface @ 16 MHz. PC-Card is the newer spec, using 3V/32 bit interface @ 33 MHz
An older PCMCIA card will work in a laptop with the newer PC-Card spec. slot (the newer slot is backwards compatible & will recognise the older type card). A newer PC-Card won't work in an older laptop with the older PCMCIA slot.
PC-Card has been the standard since around 1998 or so.
If your daughter's laptop doesn't already have WiFi built in to it then you'll need a WiFi PC-Card for it. Chances are your daughter's laptop has the newer PC-Card slot unless it's a really old lappy.
If you can find out the type of ADSL modem she already has it would help w.r.t. what other stuff you may need - if she gets broadband, that is.