I found a listing for a repeater with 0MHz offset and I don't know what to expect from a repeater like this that is different from a traditionally offset repeater.
It is most likely an erroneous listing. W7BMW does not appear as a coordinated repeater in the Seattle area, according to WWARA - the local repeater coordinating body. See https://www.wwara.org.
While the W7BMW entry might be an EchoLink or IRLP reference as noted by rclocher3, a quick check on the repeaterbook.com site of a few other repeaters shows the data is not very reliable. For example, there is an AA7SS repeater listed as 445.925 with a +5 MHZ offset. That would put the input frequency outside of the amateur radio band. According to WWARA, this repeater is in fact on 441.175 with a +5 MHz offset.
You would be well served to use a more reliable data source than repeaterbook.com.
The repeater in question is an Echolink and IRLP node, not a traditional repeater. A traditional repeater is on a mountaintop or on a tall building or tower; it simultaneously retransmits whatever it hears, so that the station calling into the repeater has the increased range resulting from the repeater's high location, expensive antenna, and high-powered transmitter.
An Echolink or IRLP node is somewhat different. It's a transceiver connected to a computer with an internet connection. Whatever the node hears over the air is sent via the internet to other users and/or nodes, and whatever the computer picks up from the internet is retransmitted over the air. Because the communication is half-duplex, meaning only one operator can talk at a time, the node only occupies one frequency, rather than the pair of frequencies that a traditional repeater uses.
It's possible to combine a traditional repeater with an Echolink or IRLP node, so that when it receives RF it retransmits the signal locally and also sends the audio over the internet, and whatever is received from the internet is broadcast over the repeater just like a locally-received signal.
Echolink and IRLP are generally used to link nodes and repeaters over the internet. (Echolink can also be used as software on a computer, with no radio involved, by users who have proved they have current amateur radio licenses.) The owner of the node in question listed his node in the repeater directory because the node is a resource to VHF/UHF operators in the area, similar to a repeater. Because the node uses only a single frequency, it's in the directory as a "0 MHz offset repeater". For North American hams, the ARRL Repeater Directory is pickier: it lists repeaters only, and not Echolink and IRLP nodes that aren't part of a repeater.
By the way, Echolink and IRLP are similar, and a node can participate in both systems, but not simultaneously. At any given time the node can participate in one system or the other, but not both.