In denotational semantics that use domain theory, a Scott domain can mean whatever we want. This is often guided by the properties of the orders used for our particular purpose.
For most purposes we can define a Scott domain to be a
This is equivalent to having a cpo that is
This class of Scott domains is closed under most type constructors, except the Plotkin powerdomain.
If we are studying nondeterminism powerdomains, then we can define a Scott domain to be a bifinite domain (aka an SFP domain). This is because SFP domains are closed under all nice constructors, including all three powerdomain constructors.
If we are studying PCF, then we can define a Scott domain to be a coherently complete cpo.