As far as I remember it is as follows:
The initiator initiates the transmission, i.e., it is the one that begins the communication - comparable with first come first serve - independent of the direction of the data flow.
In a second step, the initiator dictates the kind of transmission mode, i.e., passive or active in peer-to-peer mode, or RFID mode (reader/writer mode). The chosen mode depends what kind of modes the initiator and/or the target supports. The passive mode is used when the initiator has enough power to drive both devices (itself and target). Whereas the active mode can be used if power should be shared among initiator and target device.
When two NFC devices are put together, the device which wants to communicate first, will be the initiator. Therefore, passive devices like tags are always targets. However, there is no peer-to-peer mode between NFC devices and RFID tags.
LLCP is just a top level protocol to transmit data in either way. Therefore, the initiator asks the target to transmit or receive data. The good thing about the NFC peer-to-peer mode is, that the NFC devices can swap its roles after each successful communication.