Data roaming vs cellular data

Im traveling abroad. My international plan provides for unlimited text, $1/minute calls and some data to allow for emergency 'roaming'. Data Roaming is turned off at all times, except for when I have a specific emergency need for roaming. Question: do I also have to turn off Cellular Data to avoid international fees? Sounds like turning Data Roaming should be enough, but many on Internet suggest that Cellular Data must be turned off too. If so, why?