The Compact Flash interface is a 50-pin subset of the 68-pin PCMCIA connector. A mode pin on the interface determines whether the interface acts as a 16-bit PC Card interface or as an IDE (PATA) interface. The IDE mode of the Compact Flash provides an interface that is smaller than, but electrically identical to, the ATA interface. The Compact Flash card contains an ATA controller and appears to the host device as if it were a hard disk.
Most thin clients use a DOM (Disk On Module) to carry the system firmware. Generally these plug directly into a standard 44-pin IDE interface (or 40-pin interface in really old models).
So, using a simple passive adaptor, Compact Flash cards can be easily connected to the IDE interface. In fact some thin clients (eg the Igel 2110) use a Compact Flash card in place of a DOM for their system firmware, whilst on others (eg the Neoware CA15) the option is there on the motherboard but no Compact Flash socket has been fitted. In the latter case, if you have the necessary skills, you can add the connector yourself.
Compact Flash cards have been around since the mid 90s and, despite newer and smaller competing technologies such as SD cards, they remain popular and are used in a range of high-end consumer and professional cameras. As a result Compact Flash cards are readily available and are often faster and cheaper than their DOM counterparts.
If you decide to use a Compact Flash card there are several articles here to help you.