That distinction should be made and is often made, but at the same time it's also often made for the wrong reasons, drawing wrong conclusions that drive irrational anti-immigration.
i.e. here in the Netherlands whenever a refugee is spotted with a smartphone, that's immediately suspect and seen by one part of the population as 'This is some rich guy who's here just for economic opportunities, therefore doesn't need or deserve to be here. After all he has a smartphone'. The irony in a 'rich person' at the same time being accused of being 'lowly economic opportunist taking our jobs' I guess is lost on them.
But more importantly, it overstates 1) the indication of wealth that is a smartphone in 2015, and 2) posits it's simply okay and good enough for refugees to be safe even if they live in a tent for years in a refugee camp devoid of normal livelihoods, jobs, education, entertainment and an outlook on the future.
In terms of 1) smartphones are incredibly cheap and ubiquitous. They're also one of the most functional pieces of equipment one can have with them, for anyone but perhaps especially a refugee. The ability to communicate with lost friends and family to prevent total disappearance of personal networks due to the war, the ability to organise everything you need to do, access to information etc. It's crucial. And it's one of those things you take with you when you flee. If a civil war broke out in your country, would you not bring your phone? It's right up there in the top 3. And with $30 smartphones, and a healthy 2nd hand market around, is it that surprising to see a refugee holding a smartphone every now and then? Yet this is blown up to some kind of 'underserved richness' in a lot of European discussions.
2) Think about who those people in Turkey are who want to come to Europe 'only for economic purposes', as if that type of desire is trivial, as if not everyone deserves that kind of life. Consider that the civil war in Syria has been waged since 2011. Imagine you lived in a tent in some camp since then, living out of a bag, holding no job, getting no education, not getting anywhere in life and seeing your country still torn up and worsening by the year. Now imagine there are 2 million of you in Turkey, 1 million of you in Lebanon etc, in a camps like this one
https://upload.wikimedia.org/wikipedia/commons/6/6f/An_Aeria...
And somehow we say that Europe must remain closed to these people. That such a camp in Turkey is good enough and that if you're spotted with a smartphone, or coming through Turkey, it must mean you're not in need of anything and it's simply okay to close the borders. Where is the compassion for millions of refugees who want livelihoods just like we do?
Now if you want to pay more attention to those stuck in Syria, great. I applaud it and support it. But if they're stuck in Syria they're not immigrants from Syria, so I don't see how you'd 'differentiate between two groups of immigrants' when one is an immigrant, the other is not. And I also don't see how the group that does make it out and happens to have a cell phone and happens to aspire greater dreams than living in a tent in a refugee camp deserves our scorn rather than our sympathy. (totally not saying your post is anything like this, but you brought up points that I hear every single day from the most xenophobic people in Western Europe for the wrong reasons and it's pretty sad.)