Firewire is the Apple trademarked name for the IEEE 1394 connectivity standard adopted before the IEEE ratified it as a standard.
Originally, to use use the name 'FireWire', you had to pay Apple a licensing royalty. In the begining levied fee was One US Dollar per port, but in 2000 they recended this to the flat fee if one USD per device. Under the old structure, a manufacturer of 4-port FireWire hubs would have to pay a 5 dollar royalty on each hub (4 downstream and 1 upstream ports); under the newer scheme, it is one dollar flat regardless.
However, in June of 2002, the 1394 Trade Association officially adopted the FireWire trademark as its brand identity for the IEEE 1394 standard in what is known as a "no-fee license agreement" from Apple. This allows the 1934 group and anything that uses 1394 to use the FireWire trademark and logo free-of-charge. This is hoped to clear up the confusion between 1394's many identities.