Monitor mode enables a wireless nic to capture packets without associating with an access point or ad-hoc network. This is desireable in that you can choose to "monitor" a specific channel, and you need never transmit any packets. In fact transmiting is sometimes not possible while in monitor mode (driver dependent). Another aspect of monitor mode is that the NIC does not care whether the CRC values are correct for packets captured in monitor mode, so some packets that you see may in fact be corrupted.
Promiscuous mode allows you to view all wireless packets on a network to which you have associated. The need to associate means that you must have some measn of authenticating yourself with an access point. In promiscuous mode, you will not see packets until you have associated. Not all wireless drivers support promiscuous mode.