According to Osho, there is a clear difference: watching is superficial, like looking at television; witnessing is a deeper, qualitative shift where awareness turns back on itself. You not only see the object, you notice yourself seeing. This double awareness is meditation itself. Dogs can watch; only a conscious human can witness—hence witnessing, not watching, liberates.
Watching is looking at something; witnessing is also noticing yourself looking—and that mindful noticing is what meditation means.