Is there a standard definition for "assembly polishing"? Is there a standard definition for "assembly polishing" in the field? 
Is there a standard definition for what polishing algorithms do? 


My understanding of "polishing" is strongly influenced by Pilon:

Whereby users input a reference FASTA along with the BAM of aligned reads against this reference FASTA. The polishing algorithm then does alignment to discover local misassemblies and other alignment inconsistencies. These are then "corrected", i.e. "polished".
In long-read assembly, "polish" refers to the step to improve the base accuracy of contig sequences. I believe the terminology was originated from the HGAP paper:


  The final consensus–calling algorithm Quiver, which takes into account all of the underlying data and the raw quality values inherent to SMRT sequencing, then polishes the assembly for final consensus accuracies in excess of 99.999% (QV of >50)...


Pilon was published more than a year later and in fact, neither its paper nor README mentions word "polish".

By the way, "error correction" refers to the step to fix sequencing errors in raw reads, not in contigs. In Canu/HGAP/Falcon, that step is done by pbdagcon or falcon_sense.