The refugees and migrants who arrived after the cut-off date of March 20 have different options than those who landed on Greece's shores before the EU-Turkey deal came into force.
But in either case the options available are not what they hoped for.
We were on the shores of Lesbos just three hours after the deadline passed and saw a rubber dinghy carrying at least 40 Syrians - mainly families - arrive.
"We don't think we will be sent back. We are coming from a war-torn city [Aleppo] - of course we will not be rejected," Abu Moustafa told us.
But he could be deemed inadmissible. Syrians could be sent back to Turkey because under the deal it is considered to be a "safe country", according to the European Union asylum office, which is in charge of analysing the cases.
Those returned will see their protection status in Turkey granted or renewed
The asylum process is a relatively short one. It shouldn't take longer than two weeks, and that includes the right to appeal to Greek authorities. But with thousands of applications, it will take time before getting an appointment.
"At the moment we are analysing 50 cases a day, but we hope to double our workforce to speed up the process," Jean-Pierre Schembri, from the EU asylum support office, said.
The options that post-March 20 arrivals have are not to apply for asylum and be deported, or to apply for asylum that could be rejected or accepted.
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But if they are accepted, it doesn't mean they will be relocated to another EU country.
They will be granted asylum in Greece and provided with a travel document. That is not what many risked their lives for. They want to reach richer countries in northern Europe.
And some want to be reunited with their families who already arrived further north when the refugee trail was still open. For the time being, discussions are continuing if the relocation programme will apply to those who are considered admissible.
One case involves a young woman who we saw talking to her mother through the fence at Moria detention centre.
"I arrived late and my mother arrived before March 20. I am locked up and she is not," the Syrian Kurdish woman told us without giving her name.
"My mother applied for relocation to Germany since my brother is there. She may be accepted. I can either be deported back to Turkey or just given asylum in Greece."
Those who arrived in Greece before the EU-Turkey deal are not in detention centres, but they are stranded nevertheless.
They number more than 50,000. Some 12,000 have been living out in the open close to the Macedonia border. They couldn't continue on the migrant trail when countries further north shut their borders more than a month ago
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Their choices are to apply for Greek asylum, apply to the EU relocation programme - or leave. Again, this is a huge operational effort that hasn't begun in earnest.
And the relocation programme has only accepted a few hundred cases in the past six months.
The EU has made it clear its intention is to stop the flow of "irregular" immigration to the continent. The recent deportations back to Turkey were clearly a message.
But the expulsions and the new rules have not stopped the arrivals.
At least five people - including a child - drowned on Saturday after their small vessel carrying Iraqis and Afghans capsized in the eastern Aegean Sea.
The refugee flow may have slowed compared with previous months, but statistics from the Greek migration office show there have been 638 arrivals since the deal took effect, with the first deportations on Monday.
That number is more than the 326 people who have been deported.
And since the deal came into force on March 20, EU statistics show more than 6,000 people made the short but dangerous journey across the Aegean.
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| First boat of refugees arrives in Turkey from Greece
Source: Al Jazeera