Yes it makes a difference. Report filters are not view parameters.

The URL arguments for parameters are: &FParm#_ where # = the number of the parameter 1..10.
You still can't pass two date values for use with between operator in a single parameter. You would need to define 2 @PAR#@ in your view and write something as below, and pass two parameter values on the command line.

Where My_Date between @Par1@ and @Par2@
Please note that I did not place quote marks around the parameter names! When these parameters are typed as dates in the view design, Dynamic will add the quote marks around the date values, otherwise the parameters a strings and you must add the quotes youself. Dynamic will replace its symbolic name with the actual string value.