Turning off data roaming - - kills data transmission with anybody except your carrier.
Turning off cellular data - - turns off all cellular data transmission/reception and triggers the data roaming toggle off at the same time (the roaming switch actually disappears when cell data is turned off). Cellular voice remains operative.
Airplane Mode - - The switch that should have never been. It was developed in response to a since-disproven fear that phone electronics could screw up an airplane. Moving the switch shuts down all electronic transmission and reception (data and voice) making the machine nothing more than a tape player or game gizmo or word processor. To get any data/voice feature back, with airplane mode on, you must individually toggle that feature.
As far as international use - -
. leave airplane mode alone
. turn off cellular data
. You'll still have a functioning phone, wifi, gps, etc, - - but you won't have data charges. Obviously you'll have voice charges if you use the phone in cellular mode.
. If you decide you need a quick burst of data for some reason, flip it on, use it, then flip it back off. You will have accomplished your objective with one switch instead of having to reset several with the consequent potential costly sequential error.
Cellular Data Use:
As note above, the time may come when you need to use cellular data briefly. When the switch is off, data is accumulated in the far neverlands and not sent to your phone so you are not charged for it. When you flip the switch, the floodgates open and all stored crap pours in. There's a work-around. Your phone has a 'push' selection for notifications on each app. Make sure all of these are turned off prior to departure.
Email will be the biggest offender, most likely. A batch of accumulated mail, especially if it's graphics-rich, will be a big data burst. It's simple to switch your email from 'push' to 'fetch' to prevent this from happening. Remember that when you get to a wifi spot, you'll have to click the email icon to get your stuff. Nothing else is required except the initial push/fetch setup. What'll happen is that the bubble showing number of unexamined mails will not move until you tap the icon to open the app.