Hi, when it comes to trader insurance, YES, there are slight differences as to who is insured and for what. In the UK anyway!
Street Food Traders in particular are often caught out by going for cheap public liability insurance, 'covered' under 'membership' schemes, with industry organisations, only to find out, at their cost, that they are not covered for certain types of events.
Some traders may also need product insurance as well as PL insurance. Employee insurance is not something you really need to worry about as an organiser, that's more an in house issue for the trader, but, I tend to check they cover their staff under their risk assessment.
Check their risk assessment covers the welfare of their staff, set up and break down.
Hope this helps,