What type of agreement is the Iran Nuclear Deal considered to be by non-US countries and how does that affect the agreement as a whole?

Question

Following President Donald Trump's announcement today that he would not recertify the Iran Nuclear Agreement (JCPOA) and was withdrawing the US from the deal, I was interested to learn more about what made it possible for the POTUS to exit the agreement so easily. In exploring this topic, I found a related question on SE that explained that the JCPOA was an Executive Agreement rather than a Treaty under Article II of the US Constitution. An answer to a different SE question explains some of the differences between these two kinds of agreements.

These answers only appear to reflect the definition of international agreements in the US, though I'm sure other countries have analogous rules or laws. This left me wondering about how the respective governing bodies of the other signatories to the agreement addressed the status of the agreement, and when/how this distinction is made. Thus, I have a few questions...

Question(s)

1. Does the JCPOA have a similar 'non-Treaty' status for the other governing bodies involved?
2. How is it decided what kind of agreement will be made when multiple signatories are involved and each government might have a different definition?
3. Is it possible that a given agreement could be a Treaty in one nation, but not in another?
4. If they desired to, could the other governments included in the JCPOA (particularly Iran) simply decline to continue to participate like the US has?

Correction (05/14/2018)

According to the answer given to a different question related to the JCPOA, the Iran Nuclear Deal was not actually considered an Executive Agreement in the US. This is clarified further by this article which cites a letter to the US Congress from the US State Department which stated that the JCPOA was a non-binding Political Commitment.

Answer 1

What you are referring to as the "type of agreement" the treaty is is mostly an internal matter for the vairous countries as to how they implement the agreement negotiated between the various parties.

All the countries involved in JCPoA got together and agreed a set of measures they would all implement. How that set of measures is then enshired in each country is largely an internal matter and is going to vary from country to country as they each have their own laws and governmnet structure. Each country will have different rules and procedures determining who is allowed to make such agreements and who is allowed to nullify them (and the procedure to follow).

In the case of the US it was done by technically keeping sanctions in place and having the president periodically sign a waiver on their enforcement. This was done precisely to make it easy to re-impose sanctions against Iran with a minimal delay if deemed necessary (since sanctions are not being imposed, just existing ones being enforced). Other countries may have chosen to remove sanctions, requiring a new set of sanctions to be created if they are later deemed necessary, which probably requires more legal steps.

For Iran's side of the deal, I'd guess there isn't a single well defined act that codifies Iran's agreements that can be revoked. You probably don't need formal government act to stop enriching uranium or to allow inspectors in to facilities (although depending on the political setup, you might). You just need the people with the authority to make decisions to order that urianium enrichment is stopped. So Iran's approach to the treaty is more likely a set of actions that it is taking or not taking, rather than a legal framework. And the other signatories then look at Iran's actions and decide whether they think it is in compliance with the provisions of the JCPoA.

So to answer the specific questions:

1) The distinction between treaty and non-treaty status of JCPoA is specific to the US's governmental structures on where various powers reside

2) The kind of agreement is mostly up to individual countries, as long as what they actually do is in compliance with the agreement. Countries might care about how other countries implement an agreement internally insofar as it has an effect on how easy it is to change the deal, or indicating a degre of committment to the deal

3) See 1). The distinction between an article II treaty and an executive agreement is specific to the US constitution and doesn't apply to anyone else.

4) Yes, absolutely. JCPoA is an agreement that all parties have 'voluntarily' entered in to ('voluntarily' in the sense of perhaps reluctantly deciding it is better than the immediately available alternatives). Iran can quit the deal by simply not allwing inspectors in or by building more centrifuges than the deal allows. There is no global legal framework that enforces deals between nations.