Kismet is used as an example for BOTH modes in the two Wikipedia
articles. I would call it a passive sniffer and thus use monitor
mode.
This tangled mess is much like NAT and PAT. Everyone calls it NAT,
but it's really PAT. Sigh.
With promiscuous mode, the way it works is after the client (sniffer)
associates with the access point and exchanges WPA encryption keys, it
usually just listens for traffic with itself as a target MAC address
and discards traffic addressed to other MAC addresses. What
promiscuous mode does it eliminate this filter, and let the wireless
card decode everything that it hears including traffic destined for
other client radios. Because an encryption key is exchanged, all the
captured traffic is decrypted. However, that applies only to WPA-PSK
(pre-shared key) where everyone uses the same key. With WPA-RADIUS,
every clients key is different, so only the traffic to/from the client
is readable.
In monitor mode, there's no association with an access point, and no
encryption key exchange. The client radio just sucks up everything
that it hears, encrypted data packets, broadcasts, management packets,
etc. After all this stuff is captured and saved to a file, it is
decrypted using one of several utilities.