Or, how does the bowel keep them separate enough that one can fart without defecating.
Also, what’s the technical term for farting?
The technical term for farting is flatulence.
While it is true that releasing gas from the anus is called flatulence, there are differing processes that occur within the bowels that determine the type of flatulence and the term to associate with the release.
Flatulence is the catch-all term for the release of gas but the sub-types are referred to as farts and poots and within these subtypes the flatulence can be further defined as “ninja farts” and “ewws” and “aahs”.
Using the following definitions of the subtypes of flatulence we can describe the release in such a way as to fully convey to the observer of the release exactly what type of release was observed. The observer can also use the term to rate or critique the release in question.
Definitions-
Poot - A release of gas from the anus where the gas has went around the feces and exits the anus. A poot will pick up very little of the odor of the feces as the surface of the feces, or skin, has not been disturbed. Poots exit the anus at much lower pressure and with a faint whistling sound.
Fart - Similiar to the poot but the gas passes directly through the feces and exits the anus, often accompanied with fecal material or “shrapnel” and a loud, razzing sound similiar to blowing into a tuba mouthpiece.
Aahs and Ewws- These sub/subtypes of flatulence are differing forms of the farts. The primary element of each is the end users ability to control the release of shrapnel in the act of emitting a fart. Basically, if the shrapnel is contained within the body the fart is an “aah”, otherwise it is an “eww”.
Ninja farts - A true fart, as observed by the smell, but are released in a pooting fashion at low atmospheric pressure and are not heard by the observer. A ninja fart or the attempt thereof is the primary reason an “aah” turns into an “eww” and should not be attempted by amateurs or those dressed “commando”.
Ninja farts are also known as SBDs Silent, But Deadly. 
Excuse the pedantry, but … “has went”? I mean, come on.
Back to the OP, the answer is that unless feces gets so thick and hard that it completely blocks off the bowel - in which case you need hospitalization and it ain’t pretty - gas easily bubbles its way around and through what is in the rectum. The sphincter muscles can easily hold back a solid or semi-solid mass but gas can find its way through incredibly tiny holes. Even a pinhole opening is enough to let flatulence through.
Simple answer: Toots the horn to pass.
The escaping gas then deposits the accompanying residue in the form of “fart art” and “skid marks”, or, if misdiagnosed, Lumpy gas.
Bu-u-ut… if you have a ?stool sitting in your rectum, how does the gas get past it so that you can ?flatulate several times before the stool bumps up against your anus?
Also, I was looking for the verb form of fart (hence “farting”) - anyone know it?
It just sidles past. The walls of the rectum are flexible, so it’s not like the gas is permanently stuck in a rigid tube behind an immovable mass of faeces.
I fart
You fart
He/she/it farts
We fart
You fart
They fart.
It’s a verb and a statement of our essential humanity.
As linguist Willard Espy once wrote, when you think about it the sphincter is the smartest part of the human body. You try holding a mass of solid, liquid and gas and releasing only the gas.
Simply imagine a bubbling mudpot. Something like this,
Look at the dingleberry with binoculars. What a strange person.
“Also, I was looking for the verb form of fart (hence “farting”) - anyone know it?”
Per friedo’s answer… flattulate.
Not much of a trick to farting sans the pooh… just open your sphincter wider than a gas molecule and tighter than the end of your blunt.
Dictionary.com has no listing for flatulate.
I was looking for the technical term, e.g.:
shit is to faeces is to defecate
piss is to urine is to urinate
fart is to … is to …
Flatus is the technical noun form.
For my personal amusement, please conjugate that in Latin. k thx.