Well the first definition I've managed to google does say "permanent place of work" as part of the definition of commuting. (Confused.com)
I remain doubtful that insurance companies's definition of permanent place of work is the same as HMRC's though. Though no doubt they'd like us all to pay for the most expensive cover, even if we don't need it.
From a risk point of view, I think insurance companies want to distinguish between those who travel to the same destination every day, and those who travel to different destinations, and possibly multiple destinations within a day. The latter two is what I think business cover is for. (In fact on other sites there seem to be up to three levels of business cover, however they all seem to apply to something other than commuting to the same place every day.)
Reading on, confused.com does say that business cover is for when you need to drive somewhere other than your "normal place of work". (No, I don't think "home" is a contractors normal place of work, unless they work more days there than they do in a single client office. And even if the did, home possibly doesn't count for insurance purposes, it would make no sense to charge someone more for driving to the office two days a week than you would charge them for driving there five days a week.)
So, taking the descriptions at face value, you don't need business cover to drive to your "normal place of work", but commuting cover only covers you to a "permanent place of work". So there is a contradiction if you rely on the tax definition of "permanent."
The second place I googled was Admiral, which had the same definitions, and the same potential/apparent contradiction, as confused.com.
Third place: Allianz. Commuting is travelling to your "usual place of work."
Fourth: GoCompare, agrees with first two.
My own insurance company doesn't appear to have any definition of commuting, that I've found so far. (I work from home five days a week, so not really an issue.)