Mike Sigman promotes IT to develop IS (internal strength) and Dan Harden uses the word "aiki." Are these two things the same? I know that the two gentlemen have some differences of opinion, but do they agree on the result of IT?
Also, how would one know if someone had mastered IS/Aiki? What are the specific things they can do?
Well, look at Tohei's "ki tests" and Ueshiba's many demonstrations of the same phenomena.... they refer to it as "ki" or "ki strength". The term "ki" was originally used in Japanese to mean the same things "qi" means in Chinese: like so many other things, what ki is and what ki does has been established for a very long time.
Sokaku Takeda taught a form of aikijujutsu. He demonstrated ki skills and the use of ki skills to perform "aiki" is an old concept in Asian martial arts. The only confusing thing is the number of terms people have used in various arts (both China and Japan) to refer to those basic skills. So whatever personal skills Takeda demonstrated in terms of ki skills, they were based on the known ki skills from very far back. BTW, "Ju", as in "jujutsu" seems to also refer to "internal strength":
The soft or internal arts were known popularly in China as jou-chuan, the characters for which are read in Japanese as "ju-ken," meaning "soft fist." It was common throughout that period to refer to all internal arts by this name. This may have played some role in the eventual popularity of the term jujutsu for these rough-and-tumble martial arts. Kano and others argued that there was nothing "gentle" or "soft" about Jujutsu, and that ju was hardly the over-riding principle of the arts. The arts were called "ju-arts" or jujutsu because they were based on internal methods and ki (internal energy), not because they employed no strength or force
The training of internal skills is done with internal exercises aka "nei gong" and the styles that specialize in those developments are the "internal styles" aka "nei jia". They develop ki/qi skills and use the dantien to manipulate those skills. "Aiki" is just another term for the usage of those skills in a blending manner with an opponent's forces.
I think that sometimes the conversation is so Aikido and Daito-ryu focused that people lose sight of the fact that these skills have been around many hundreds (probably thousands) of years and Takeda didn't originate the skills, even though he certainly developed his own personal take on them in regard to the martial abilities he had. I.e., Takeda got his ki skills from someone (probably his father) and he worked on them and developed them as he did.
So, yes, we're all talking about the same things, generally. The only caveat that I repeatedly make is that there is a whole spectrum of levels and gradations of these skills out there. I.e., no two people had exactly the same abilities (think, e.g., Ueshiba and Tohei) in the same way that there are, for instance, guitar players who play blues, some play classical, some jazz, etc. Continuing the guitar analogy a bit, let's say that Ueshiba played classical guitar Aikido and that Tohei plays neo-Flamenco Aikido... people have to be careful and make sure (i.e., do thoughtful practice) that they don't wind up grabbing a guitar but playing Bluegrass Aikido.