"Does our Constitution adhere protection unto those of other Nations that are NOT under US jurisdiction"
No.  However.
"attempting to come here?"
If they do so legally, ie. apply for a visa or covered under a treaty agreement such as provided to European travelers and visitors to the US then yes.  One area of exception though is ambassadors and others (such as family) who are granted diplomatic immunity.  For example, the Constitution provides for Congressional (and by delegation Executive) decision making that can be on any rational ground but cannot be capricious and arbitrary.
"Do they the both of them receive the same protection under our own Constitution?"
Yes they both have similar procedural and substantive rights (though limited) even as non-citizens within the US.  Outside the US is different based upon circumstances.
"If so, why?"
A key distinction is that the Constitution does not grant protections to citizens but _limits_ government action.  
More (character limit).