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Difference between inet and cidr

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May I know what is the difference among cidr and inet? I read through Network Address Type (http://www.postgresql.org/docs/8.3/static/datatype-net-types.html)

"""
The essential difference between inet and cidr data types is that inet accepts values with nonzero bits to the right of the netmask, whereas cidr does not.
"""

I understand what is Subnet Mask from http://en.wikipedia.org/wiki/Subnetwork. But, what does it mean by "nonzero bits to the right of the netmask"? Is there any example to show the difference among the 2?

If I provide the following input 1.2.3.4, this is what I am getting if I view through pgAdmin.

inet = 1.2.3.4
cidr = 1.2.3.4/32

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