SSR altern symbol why
The '~' (tilde) symbol tells you that it is for AC.  Internally it is using a triac and these are only suitable for AC switching. 

The -| |- symbol represents a normally open contact and is common on North American electrical schematics.

The 24-380VAC text indicates that it is rated for switching voltages in that range (which excludes DC).



Counterfeit Fotek SSRs

It appears that you are considering Fotek SSRs. Read this first: 
UL warns of solid state relay with counterfeit UL Recognition Mark (Release 13PN-52).

See also Big Clive's Teardown of an eBay 25A Solid State Relay (SSR).