There is a difference there even if no one wants to admit it. The difference is between one who was never Catholic having to go through at least a few months to a year of instruction and THEN become a member of the Church before finally being absolved in confession, and a Catholic who has to make an abjuration of heresy, even if that's before the whole world, and then be absolved in confession.

Fr. Luther only had to abjure his heresies to be absolved - yet, he remained a Catholic priest in the sin of heresy through it all. And yet the no good heretic could still do what all Catholic priests do, namely, administer the sacraments in dire emergencies. Since his death, it is to his everlasting shame that he will always be a Catholic priest for all eternity. The evil excommunicated heretic, apostate and schismatic that he was, he never ceased being a Catholic priest. 

A Catholic who is guilty of  heresy commits a mortal sin. Heresy is the worst of all the sins, that is what heresy is, a sin. The only way a Catholic can be absolved of mortal sin is through confession. 

IF the censure attached to the sin requires an abjuration then so be it, once completed in what, 60 seconds? 2 minutes? 3 minutes? they then would walk right into the confessional to be absolved exactly the same as you and I and all Catholics have done all of our lives.

Whereas as typically, the priest always presumes our contrition and firm purpose of amendment prior to absolution, the censure attached to the sin of heresy requires the heretic to profess as much with the abjuration, privately or publicly. 

Compare that to a heretic who was never Catholic and wanted to repent. Before they could go to confession they would first have to become a member of the Church through all the usual catechetical instructions etc.,

This is basic Catholicism, it is not complicated. It really is not the least bit complicated.

I get your point of course, but you are mixed up.

 Yes, an excommunicant can simply go to confession - depending, as I already said: "it depends on the authority [who issued the penalty], the heretic and the censure that is attached to the sin, and if it is reserved to the Holy See, or to the bishop, or whatever other penalties/requirements are part of that censure."
 
Otherwise, why, in the traditional formula of absolution in the Sacrament of Penance, is there is a general absolution from the censures  of the Church? It is because an excommunicated heretic can simply go to confession - depending on what I said above in italics - have the censure lifted and then be absolved by the priest.

I supplied the definition from Canon Law's Commentary on what a censure is. You change it from that to "a low level canon law punishment." Better to stick to what the commentary says Pax, it's plain and clear, your idea of what it is is your idea.

So Deo Gratias now that the penitent heretic pope or cardinal or layman or whomever went through the "formal process," he is still a heretic because all the heretic did was essentially promise to repent, made a profession of faith and promised to be faithful till he dies. Right? HE IS STILL A HERETIC BECAUSE HE STILL HAS THE SIN OF HERESY ON HIS SOUL BECAUSE HE HAS NOT YET BEEN ABSOLVED. Here you need to admit that the "formal process" does not absolve anyone from their sin of heresy.

So lets say that Catholics in the sin of heresy are outside of the Church 

- if that is so then he cannot partake of the sacrament of penance even after completing the "formal process", not even to the pope, because having the sin of heresy on his soul he is still not a member of the Church because he is still a heretic. No abjuration or "formal process"can absolve him from that sin.

I am saying "formal process" or not, he is still a heretic until he receives absolution - the only way for that to happen is for the heretic to walk into the confessional and be absolved exactly the same as only members of the Church are permitted to do.

I misspoke.  A censure is a general term.  An excommunication is a TYPE of censure.  All excommunications are censures, but not all censures are excommunications.

I never said the formal process means that he is forgiven, but...it is a sign that he's repentant.  Which is a necessary sign/step, per canon law.

Heresy doesn’t take away the priesthood.  

Notice the definition above uses the phrase "communion of the faithful".  If someone isn't part of the communion of the faithful, then they aren't a member.  THAT'S THE ARGUMENT.  How can one be a member if they aren't part of the faithful?  A catechumen isn't part of the faithful, and that's why they aren't a member.

As I explained, if one just leaves it at that, saying "a heretic isn't a member" then that is a partial truth.  Because an excommunicated person, IS still a catholic, but not a member of the Church.  THAT is the distinction. 
Irrelevant to Church law.  The distinction you are making is in regards to the internal forum and their degree of guilt for the sin.

But in regards to canon law, V2 heretics are equally as guilty as Luther.  In fact, V2 clerics would be MORE guilty because Luther was a simple priest, while V2 clerics are more educated, more learned and have more graces of state.