ok, lets start in the beginning- he vomits 4 hrs after he ate? how often does he eat? is it same food all the time? what about threats?
Lets start with basic anatomy- food thrown up short time after eating and looking very undigested is coming from stomach itself, food that somewhat digested and comes about 4 hrs later is probably from small intestine upper parts, and anything that looks like fecal mass but still tooo moist is probably from lower digestive track, coming about 6-8 hrs after eating.
Stomach/ pancreatitis may give you what they call projectile vomiting when vomit flies a distance.
What you are concerned is how is Smudge otherwise- does he has same level of energy, is his tummy distended, is he pooping, when you touch and press on his tummy does he tell you it is painful, what his poop look like, does he drinks and eat still the same level he normally does, does he have a fever...
it may or may not be connected to the problem he used to have before.
Your pics show some large parts of something on the bottom... what is it?
Che just went with a bout of vomiting started after he digested few foreign objects, then he had vomited for 3 nights in a row... but otherwise he was his usual self... therefore we did not go to the vet...it stopped same way it started... but I can understand you, I was feeling anxious too...
To be honest..if he had not had the issues before I would not worry at all. Dogs throw up all the time. Nothing to go crazy over, except Smudge did have the bad episode earlier.
To answer some of your questions:
1. He is acting fine and going to the bathroom fine. The same as last time. Had the vets completely fuzzled.
2. The large thing at the bottom is a chicken beggin strip.
You didn't ask this, but I will offer the info up anyway.

In this last 24 hours Smudge has had:
4 meals (midafternoon and late night)
2 hot dogs
1 chicken strip
water
2 beggin strips
3. His meals are not always at the same time, because my work schedule does not allow it. Sometimes I work the early shift, and sometimes I work the mid shift or night shift.
If the chicken strip was fried, that could cause issues. Raw, boiled or grilled chicken wouldn't necessarily have upset his stomach.
what is in the breading?