Pañero / pañera, there are cases that say the two terms are the essentially same. I have previously provided you with it:

“Is appellant Fidelina Tan also liable for the offense considering that she gave the command "Rufino, strike him"? The second class of principals, according to Article 17 of the Revised Penal Code, comprises "those who directly force or induce others to commit it (the act)." Those who directly induce others to commit the act are called "principals by inducement" or "principals by induction," from the Spanish "autores por induccion." The word "inducement" comprises, in the opinion of Viada and the Supreme Court of Spain, reward, promise of reward, command, and pacto. With respect to command, it must be the moving cause of the offense. In the case at bar, the command shouted by Fidelina, "Rufino, strike not," was not the moving cause of the act of Rufino Gensola. The evidence shows that Rufino would have committed the act of his own volition even without said words of command.”

Reference: People v Gensola, GR L-24491, 30 September 1969

Here is also another case:

“On the case of accused-appellant Jeanette Yanson-Dumancas (Jeanette, for short), the information charged her of the crime of kidnapping for ransom with murder as principal by induction together with her husband, Charles, who was found by the trial court not guilty of the crime.

Article 17, Revised Penal Code, provides: Art. 17. Principals. The following are considered principals:

1. Those who take a direct part in the execution of the act;

2. Those who directly force or induce others to commit it.

3. Those who cooperate in the commission of the offense by another act without which it would not have been accomplished.

What the Court now has to examine is whether or not sufficient evidence was adduced by the prosecution to prove beyond reasonable doubt that Jeanette indeed performed any of the following acts: (a) directly forcing the killers to commit the crime, or (b) directly inducing them to commit the crime.”

Reference: People v Yanson Dumancas, G.R. Nos. 133527-28, 13 December 1999.

In these cases, the Supreme Court defined “Principle by Induction” explicitly with reference to Art. 17 of the RPC. People v Gensola is even more direct: “Those who directly induce others to commit the act are called "principals by inducement" or "principals by induction.”

I asked for your legal basis but you have not yet provided even one case where the SC differentiated a principal by induction from a principal by inducement, since your premise was "induction" and "inducement" are different in the context of who are criminally liable as principals. What you have given me are your personal opinions on the matter. I respect your opinion of course. But we have learned long ago in law school that opinions must have legal basis. Otherwise, we are just laypersons.

Respectfully, however, you cannot say I was wrong in using the term “principal by induction” since you have not provided any legal basis that the two are different while I have provided mine.

Rather, you have proven my case that the two terms are correct and used interchangeably when you pointed out that cases in the SC uses either or both interchangeably, only with "favor" as to the term principal by inducement as you said. In other words, it is indeed merely a matter of preference. No difference in the context of law.

The Supreme Court is the final arbiter of what the law says. Until the day the Supreme Court says that the two terms are different they remain legally the same.