Why EA instead of EO?
Because every word uttered by a politician is carefully selected in custom crafted speeches. It's no accident that very little any major politician speaks out on is carefully written and screened beforehand, often with days advance notice.
Politicans, perhaps more than any other breed of human, know how the nuances and interpretations of words can be carefully groomed to say one thing while implying another entirely.
Whether or not there is any "legal" distinction between "Executive Action" and "Executive Order" in this context doesn't matter nearly so much as what is implied by the wording.
"Executive Order" implies the President is directing a specific set of actions, or interpretations which allow specific actions, to take place on his sole authority.
"Executive Action", in these circumstances, implies the President is establishing an agenda that he wants OTHERS to act on in order to get the results he wants (additional laws which he can enforce).
If he actually unilaterally directs specific actions to take place contrary to the authority he is currently authorized, then the legality of his actions would be shot down and this would do great harm not only to his standing, but his political party which supported it.
As he has currently expressed his 23 action items, they provide him with an ongoing politically charged support base which benefits him and his party by energizing activists who support that cause. It gives him "breathing room" in which to maneuver politically in order to further sculpt the political landscape in the coming months and years.
One of the lessons learned by the Democrats after the last AWB fiasco was that the political backlash cost them many seats in the subsequent elections. This is NOT a long term goal of any political party, much less the Democratic Party.
Taking the path he did allows him and his party to continue working towards stronger political positions through subsequent elections. Not only that, but remember that the President is the one who appoints Supreme Court Justices (through confirmations). This is another long term goal of the Democratic Party...and losing too many seats in elections won't help that confirmation process. And, if they should somehow NOT get a chance to appoint any new SC Justices during his term, a subsequent loss of the Presidental election in 2016 will really set the Democrats back politically.
Make no mistake...this issue with gun rights is HUGE politically...and the Democrats cannot afford to go whole-hog in taking actions which would certainly be shot down as both illegal and unConstitutional. The battlefield has thus been shifted to Congress and the many state and local governments, where smaller battles can be fought and won...or lost at great expense to gun rights activists.