I don't have much experience with echolink at all, but the way I saw it used was through a local repeater run by a club. They had an echolink node on 2m, and previous members who had moved away would sometimes randomly call in during the evening, or (more often) during weekly nets. The repeater would transmit what they sent via the 2m output frequency. I never tried it, but with the right access codes, I (supposedly) could use the DTMF keypad on my HT or base station to transmit to the repeater, and have my audio go out to a similar repeater somewhere else. The repeater would listen to all incoming RF, send it over the internet to the other echolink node, and the other node would transmit, etc. So, if someone several states (or countries) away was connected to the system, I could chat with someone using my radio gear to someone far away using their radio gear or someone connected to the internet with their computer & microphone.
Yes, the same could be done with a cell phone, but when an echolink node is hooked up to a repeater like I described, it doesn't have to be a 1:1 conversation. It basically just works like any VHF/UHF repeater (many to many).
With the cell phone app, which I haven't used, I understand it to be able to work like the following:
Say I'm traveling out of state. I could bring my HT and hope there's a local echolink node I could connect to, or bring a laptop and connect via the internet. Then, I could access the local club repeater that functions as an echolink node. But, if I don't want to pack my radio gear or a computer, I could just use my cellphone instead. It basically turns your cell phone into an HT that's connected only to echolink. So, theoretically, if there was a local net going on back home on the club repeater, I could join in on it from my cell phone, without using a radio or computer at all.
If I just wanted to talk to a single neighbor who is a licensed ham while on the road, it would probably make more sense just to make a cell phone call directly, assuming you have cell service where you are traveling. But, I think two people could talk to each other via the internet with echolink, and would work fine where you only have an internet connection, but no cell service.