I’m not a lawyer, but here’s my understanding of things - and its covered here on the forum in great detail, so I’ll try to be brief
You can purchase a stripped receiver that has never been a rifle or pistol or anything, and build a pistol. Thats ok with ATF. No extra paperwork, just the 4473 transfer form. Sounds like you’ve done that. A lot of folks take that very same receiver and apply for the short barreled rifle tax stamp (SBR) using ATF Form 1. In other words, the pistol is a step on the path to getting the SBR, since the pistol is legal to have “as is”.
To your more specifics, assuming non-SBR status, if the built up pistol is every fitted with a shoulder stock, it then becomes a rifle, and must always be thus, forever, or until SBR status is gained. So one caveat is once you have a pistol made, and then turn it into a rifle later, its a rifle. Thats it. No going back, unless you get the SBR stamp.
If you get an SBR stamp (paperwork, trust or other additional paperwork, $200, long wait) then you can more or less use the firearm as a pistol or rifle or short barreled rifle. Officially, its a short barreled rifle, and if a permanent change in status is made, you’re supposed to inform ATF. That is, if you decide to make it a standard rifle “permanently” you’re supposed to say so. However, temporary reassignments are not forbidden.
There are all sorts of ATF letters stating such out on the net - mostly listed in various forums that discuss NFA weaponry. One common misnomer is that an NFA SBR receiver is always an SBR receiver. ATF says… you can un-SBR the receiver by permanently making it a standard rifle. In that manner, you can own an SBR, and if you need to move to a non-SBR state, you can put a standard length barrel on it, inform ATF, and you’re good to go… no longer SBR, but goodbye $200.
I’m sure if I’ve fubar’d that… someone will come rip me a new one here very soon.
Hope that helps!