Recently, I came upon a source, treating the time period of the late 1930s and early 1940s and the Winter War in particular, that differentiated between "regular" infantry and "conscript" infantry of the Red Army. I was under the impression that the Red Army was a conscription army for the entirety of its existence. Was there any military personnel, especially in the infantry (discounting command and technical staff and specialized professions in other branches), that was not composed of conscripts? If so, would any of these qualify in any greater sense for being referred to as "regular" than the conscripted infantry? Or, conversely, was there any conscripted military personnel that was in any sense less "regular" than regular infantry, even if regular infantry was also conscripted? Perhaps "levies" of reservists? What distinction could be meant here?
This system wasn't around in late 30s and early 40s. It was around since 1925 till early 1939 when decision was taken to convert 'territorial' formations of the Red Army into regular ones.
So what the difference was between 'territorial' unit (which you call 'conscript' in your question) and regular one?
Regular unit was kept at the higher strength level during the peace time. Usually it had between 50 to 75% of the required personnel. And entirety of the personnel of such units were full-time service regulars. Such units were deployed alongside USSR borders.
Territorial unit was organized quite differently - it only had a small core of officers and non-coms (about 10 to 20% of official requirement for such unit) and enlisted men didn't serve the full time and only were called for training for about 1 to 3 months in a year. Territorial formations were kept in the internal regions of the Soviet Union and formed a cadre for large scale mobilization in case of war.
Some units were mixture of these two systems.
So soldiers in both regular and territorial units were conscripts but different ones. Regulars were fulltime servicemen while territorials were part time National Guard-style soldeirs.
The system was created because Soviet Union in the 20s and early 30s was unable to maintain required numbers of regular military units, so territorial system was implemented as a cost-saving measure.