Mrs R and I are planning a trip to Africa soon. She’s concerned about whether her Samsung phone will connect to wi-fi in the hotels we’ll be staying in.
I know that international telephony is a twisted mess of incompatibilities; is wi-fi like that? Or will my wife’s phone be able to connect to a hotel wi-fi network in Nairobi just like it does in a Starbucks in Seattle?
As long as they have real wi-fi, it is the same. Cellular technology is the one that differs by location but wi-fi doesn’t as long as the phone, tablet or laptop is reasonably current.
WiFi is a international standard (802.11)
No, it isn’t. I’ve never had a problem using my GSM phone from Europe to Africa to Asia. AFAIK, only the USA and Russia are “special” in this regard with more than one common protocol.
It only matters if you have a CDMA phone (Sprint or Verizon.) Everybody else uses GSM which works everywhere.
You can buy a cheap GSM burner and use that if you are unlucky enough to have one of the carriers that refuses to get with the times.
One small difference internationally with WiFi are the allowable channels and permitted signal wattages within a country.*
For example, for the good old 2.4GHz range, the US only uses 1-11 while most countries allow 1-13. If your phone is set to US standards and you are at a hotel that uses channel 13, you gotta fiddle with stuff (if possible) to access it. But that’s unlikely.
The bands in other ranges also vary. See here. So you might miss out on the higher speed, multi-band capabilities.
Just to be clear: GSM vs. CDMA has nothing to do with WiFi.
Even that’s not necessary in a lot of places.
Most phones, even carrier-specific versions, are multi-band now. My (not carrier specific) Nexus 6p and my family’s assorted Verizon Samsungs and LGs worked just fine in Japan, Korea, and the Philippines. (Voice, text, and 4G data.)
Telephony has homogenized a lot in the last decade.
And none of this ever had anything to do with Wi-Fi.
Both wifi and gsm will work in most places, but there are different radio frequencies used for both. Different governments allocate different parts of the wireless spectrum for consumer wifi and cell phones. Chances are, most recent devices (last 5-6 years for phones, last 10 years for wifi) will have no problems. They used to be sold as “quad band” or “world phones” but these days they’re just “phones”. And wifi receivers usually support all the channels, I think, it’s just the routers that have certain ones disabled in certain countries. But if in doubt, check your phone’s radio specifications and your wifi supported channels for your computer. 99% probability it will be fine.
Also be aware that some countries do not allow calls/video chats on WiFi. For example you cannot use FaceTime audio or video, WhatsApp audio/video, Skype audio/video etc. in Dubai (UAE).
Mrs R mostly wants to back up her pictures to the cloud. Our current plan is to leave her phone in airplane mode and turn on the wi-fi in hotels.
If your phone uses a SIM it is good to go in Africa (or anywhere in the world). Only the USA and a few hangers-on are anomalies in having the old CDMA system too. However, unless you have a specific arrangement, cellular roaming - and especially cellular data - can cost you bigly. I usually turn off “data roaming” unless I have the special “roam like home” deal.
As for Wifi - pretty much standard. We were chuckling at fellows from our lodge when we saw them stopped at the Ngorongoro Conservation Area entrance gate as we went by, they asked their driver to wait a bit longer so they could use the free wifi there on their iPhones, and they were from Canada. There was not wifi in the Serengeti tent camps, but if I recall, the main park office area by the air strip had it - and it worked, as did every hotel in Tanzania. Every Wifi all over the world works pretty much the same; Europe, middle east, Egypt, Dubai, India, Tanzania, Ethiopia, Turkey, China; in Australia and New Zealand I think the “wait” circle spins counter-clockwise. 
Just be aware that the next part - the router from wifi to the internet - is occasionally hit-and-miss, but I’ve had that in quite a few American hotels too. Plus, a lot of more remote places, they pay by the byte for internet so avoid big uploads and downloads at the smaller hotels. (If it’s a big chain hotel they probably have a bigger connection and better bandwidth) I say this because my camera photos were pushing 10MB per photo, so a day’s click-click-click could be pretty big for me.
Verizon using a Samsung and an iPhone - works fine in Italy, Germany and France.
There’s some misinformation and oversimplification here. CDMA phones can roam to other CDMA networks as well, and they are all over the world (but getting rarer).
GSM has different frequencies around the world and even if you have a sim card, you have to make sure your phone supports the frequencies in your destination. Same with CDMA. Just because something takes a sim card doesn’t necessarily mean that your phone will support a particular carrier in a destination country.
In practicality, most recent phones have all the frequencies necessary for most of the world, and LTE has forced all major carriers to jump onto GSM so the CDMA question isn’t as irrelevant. Verizon phones can still sometimes have a separate CDMA radio, alongside the GSM radio, but they’re getting rarer.
Tldr it will probably work fine, but if you need to be sure, double check before you go, especially if your phone is more than 5 years old or so.
Also, if you travel a lot, consider project fi for unlimited calls and data around the world. Verizon roaming plans are absolute shit.
GSM (which is TDMA) is, or was, bog-standard, with a couple of different frequency bands in use, but I don’t think UMTS or LTE has anything at all to do with the GSM standard. Did I miss something? Certainly wi-fi doesn’t.
ETA LTE uses FDMA
Sorry, I looked more into this. The confusion for me was that I always thought LTE was an upgrade for GSM and backward compatible, but that’s only partially true. It was co-developed with CDMA and GSM in mind.
What happened was that LTE’s requirement for SIM cards made it easier for even CDMA carriers to transition towards a unified worldwide LTE network, at the same time where more and more phones were getting additional radios. Together, they improved international roaming.
Before LTE, Verizon was strictly CDMA and roaming internationally would often require a loaner GSM phone (or else limited access to rarer international CDMA networks).
Then, in the earlier stages of LTE, Verizon phones had a separate CDMA radio for voice/text alongside their LTE one for data.
Now, many Verizon phones can use LTE for both voice and data, although some still have a CDMA fallback for voice. Verizon hopes to completely remove CDMA by next year.
TLDR: LTE required SIM cards while still being backward compatible with older networks, which allowed both CMDA and GSM carriers to move towards one unified worldwide standard. There are still differences in international frequency allocations, but overall the situation is lots and lots better than before.