'Parallel action', the term employed in the original query is a very 
common term not only in film criticism but among film-makers, and has 
relatively consistent meaning. However, as posts here have noted, a 
critical/theoretical consideration of parallelism and editing can be 
much broader. However as a matter of descriptive lexicography, that's 
generally not what people mean to invoke by employing 'parallel 
action' since yes, the emphasis is on the action as much as the 
parallism and thus no, cutting between Kerensky/Rooster is not 
parallel action, whatever intellectual parallels it may employ or 
evoke.

I'm reconsidering my suggestion that 'cross cutting' is a more 
omnibus term, though. (A more surely wider term would be 
'intercutting'). That is, the emphasis in 'cross-cutting' may well be 
on 'cross' -- as in intersection (or to get Eisensteinian, 
collision). In this sense 'cross-cutting' would be a sort of opposite 
to 'parallel action'. There's nothing parallel (travelling side by 
side in similar directions along separate paths) at all between the 
cossacks and the baby carriage. They are opposites, they cross, they 
collide. I still think 'cross-cutting' is a somewhat broader term 
since the things crossed can be more conceptual, whereas 'parallel 
action' in practice pretty much limits the parallelism to lines of 
narrative.

But really, it matters less what we call things -- that which we call 
a cross-cut is by any other name... -- than how we develop our 
understandings of the discourse of film. Sometimes editing just puts 
different things together to no particular effect. Sometimes it 
creates various kinds of parallels. Sometimes it creates various 
kinds of intersections. It's all contextual, conditional open to 
interpretaion and not mutually exclusive, but there surely seem to be 
different tendecies at work.

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