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Wikepedia's table Comparison of SHA functions mentions "Security(bits)" for some SHA functions. From the ratio (Output size (bits): Security(bits)), I feel it is something like "collision resistance". So,
Should we only consider collision resistance as the Security of a hash function?
what does the Security in the table mean?
Security in the table refers to collision resistance. By the birthday problem, there's a generic attack that finds collisions in any compressing function by choosing $\sqrt{2^m}$ random inputs ($m/2$ security bits), where $m$ is the output length.
Depending on the application, weaker requirements might be sufficient, such as second pre-image resistance or even one-wayness. A generic attack against the two weaker notions requires about $2^m$ work ($m$ security bits).
