I am not a lawyer or an expert on anything, but do have some experience in the Govt and am writing based on that experience. On that basis:
Seems to me that Executive Orders have a force and effect similar to regulations. As in CFR (Code of Federal Regulations). The simple view is this: most laws are conspicuously vague in the details. The law simply creates an imperative, or defines lawful/unlawful acts, or orders creation of a new program, say. Then the real work starts.
The staff of an agency designated to carry out implementation of the law then sits down to interpret and implement said law, and they write the regulations. The regulations regularly exceed the volume of the enacting law by orders of magnitude, so Obamacare, a 2500 page law, should be expected to generate more than 50,000 pages of regulations. The regulations are then published in the Federal Register for public comment for a prescribed period, then the final regulations are issued. In essence, the Regs define the parameters and rules for implementation of the law and unless challenged, they effectively become the law as most people would interpret it.
Then from the Regs, an agency creates its policy. In Govt, the doctrine is: policy can be amended or suspended usually at fairly low levels, regs can be waived for good cause but usually only by Director/Secretary/undersecretary level staff, but statutory mandates require an act of congress to set aside.
It seems an EO would bypass the whole process of public comment and have the effect of new Regulations. It could alter the implementation of the underlying law, alter the process or procedures used by the agency enforcing the law, but would not itself be a law. It could easily change the list of banned imports, or records retention from NICS checks, create a national registration program, magazine limits, etc. If the EO violates existing statutes it could be set aside if challenged, but... as with the immigration EO directing ICE to stop enforcing sections of putative valid statutory provisions, the limitations in scope of an EO is not well known. And if it goes unchallenged, it basically might as well be the law.
"To my mind it is wholly irresponsible to go into the world incapable of preventing violence, injury, crime, and death. How feeble is the mindset to accept defenselessness... How pathetic." - - Ted Nugent
"Cogito, Ergo Armitum Sum" - (I Think, Therefore I Am Armed)- - anon.