Interesting I was unaware of that distinction Fradow :)

Yup Brady, that's why I got to that conclusion. I'd have to check with a more experienced gunners, but I assume all soft-bodied enemies have the same general mechanic (can be knockdowned provided enough damage).
And I did based that on DBB, along with lots of experience with swords (there are point when when you go deeper, they just stop to knockdown).

Do the Iron Slug's bullets travel faster than those of the Callahan?
No

Do either of their bullets travel faster than those of their predecessors?
If they follow the pattern set by all the other guns (yes, even the catalyzer lines), then yes, they should.

Do they interrupt, knock back, knock down or some combination of the three?
Callahan and Iron Slug's bullets knock down what can be knocked down (Gremlins/Wolvers/Devilites/Zombies), interrupt what can't be knocked down (Turrets [slug], Jellies [slug]) and don't knock back anything... unless you charge. The charge pushes mobile monsters back 2-3 tiles.

However, and curiously enough, the Punch gun's normal bullets have very significant knockback per shot (1-1.5 tiles).

Does one or the other have better range?
No.

What are the properties of their charge attacks?
Both charge attacks knock back their owner about 2-3 tiles, but the Callahan's can stun. No status on Iron Slug.
They are powerful enough to interrupt what normal bullets can't.

Does the Callahan do as much damage to neutral targets as Iron Slug does?
Yes, exactly the same amount.
Placeholder: Now that Guild Training Halls are a thing, I'll try to grab you some numbers from the T3 one.

Went to GTH, and it confirms what I saw in FSC: They do the same neutral damage.

@Brady:
If you mean from the magnus line, no, they're not balanced with each other. Aside from a little more monster-compatibility, Callahan is better :<

I actually think the best normal-special balance is in the Catalyzer lines:
The Neutralizer's (normal) raw charge is stronger than Biohazard unless Biohazard poisons its target (so the special can do better, but only by chance).

ninja edit as response to post below:
bolded the text.

Yes, if you could please test the range of the Iron Slugs normal attack splash, that'd be great =) I am a Gomber (Gunner Bomber) so I use an electron bomb and magnus right now, so if the Iron Slug does indeed have significant splash attack from it's normal attack alone, that would pair beuatifully with my electron =)

Thanks so much!

-Styrka

The special types do less damage than the normal variant, though this is because they practically always have a status. Iron Slug vs. Callahan/DA vs. GF would be exceptions in that they don't do less damage than their counterparts, despite one also having status over the other.
And yeah, the Magnus series doesn't have a special splash attribute either; if you hit those two jellies shoulder-to-shoulder, then you hit both, like any typical Handgun splash.

Would also like to note that Callahan can Stun on normal hits, since I didn't see it mentioned.

The splash damage on the Iron Slug appears to be a myth.
I thought the splash damage was a thing that applied to the max-range explosion of the normal shots.

You mean like when using guns to break grass patches? I was under the impression that every gun could do that, with splash damages. Having no splash damage at all would imply that Magnus' can't do this; could be something to test. If it definitely has no splash on a hit then maybe its splash is limited to a certain range threshold?