Hi. Ok, ready? ... Here's the knowledge :
1) Because when "older people' were using stuff on a computer they were not permanently connected to the internet through a router / modem, they actually had to tell their computers to DIAL OUT WITH THEIR MODEM.
2) A phone was a phone, not a cameraphone, not an MP3 player, not a GPS, not a Youtube device, not a Snapchat / Twitter / Instagram / Tinder / Fortnight / Facebook, Tindr posting app machine, IT WAS A PHONE - and it required wires in the house or under the ground to payphones in public.
3) There were a lot more choices of things to with Your computer back then because when You DID tell Your modem to dial out to other computers (Your internet modem only contacts a server from Your ISP - look it up) it had the option of dialing any phone number in the world, which could've had a fax machine, TTY device (Deaf people used them), another modem with a computer either hosting & / or receiving files, or even a full-fledged BBS with thnigs like chat groups, FORUMS, Usenet newsgroups, multi-user online games NOTHING like they are now, and so much more.
So when they say "On the computer" it means "NOT on a smartphone or pen and paper". And when they say "on the internet" or "online" it means connecting to somewhere besides Your own home.
There was also a HUGELY popular service called AOL. It was kinda what Facebook strives to be today with all their added games & services, but they don't seem to get the similarities, and foresee the problems AOL had when they rolled out each new feature.
"Back in the day" going online required a few steps & took a huge amount of time out of Your day.