What is the difference between toGMTstring() and toUTCstring()?

GMT and UTC are different timezones, they are Greenwich Mean Time and Coordinated Universal Time respectively. GMT is a 'solar' timezone, whereas UTC is 'atomic'. For most purposes they are essentially the same thing, however UTC is more 'universal'.

Interestingly the documentation you point to for toUTCString still show a GMT output:

var today = new Date();
var UTCstring = today.toUTCString();
// Mon, 03 Jul 2006 21:44:38 GMT

For interchange of data between application I would prefer to use something like ISO8601, which uses the 'Z' suffix for UTC:

2013-01-16T08:19Z

Where the 'Z' confusingly stands for 'Zulu time'!