apt upgrade vs full-upgrade vs dist-upgrade

The three differ on one axis: how much apt is allowed to disturb to get you the newer versions. Two packages here have upgrades waiting. tips-tool 2.0 needs a package that is not installed; tips-app 2.0 needs one that cannot be installed while tips-legacy is present.

apt-get upgrade will not install a new package under any circumstances, so both stay where they are:

apt-get upgrade -s

Reading package lists...
Building dependency tree...
Reading state information...
Calculating upgrade...
The following packages have been kept back:
  tips-app tips-tool
0 upgraded, 0 newly installed, 0 to remove and 2 not upgraded.

"Kept back" is that refusal, and the troubleshooting page covers what to do about it when it happens on a real machine.

apt upgrade is not apt-get upgrade

The apt front end changed the rule. It installs new packages when an upgrade needs them, and still refuses to remove anything:

apt upgrade -s

Reading package lists...
Building dependency tree...
Reading state information...
Calculating upgrade...
Upgrading:
  tips-tool

Installing dependencies:
  tips-helper

Not upgrading:
  tips-app

Summary:
  Upgrading: 1, Installing: 1, Removing: 0, Not Upgrading: 1
Inst tips-helper (1.0-1 stable [all])
Inst tips-tool [1.0-1] (2.0-1 stable [all])
Conf tips-helper (1.0-1 stable [all])
Conf tips-tool (2.0-1 stable [all])

tips-tool upgraded and pulled tips-helper in with it. tips-app is still held, because reaching its new version means removing tips-legacy, and no upgrade of either kind removes a package.

So advice written for apt-get does not transfer. A guide from 2015 saying "upgrade never installs anything new" describes a command that is still on your system under a different name.

full-upgrade is allowed to remove

apt full-upgrade -s

Reading package lists...
Building dependency tree...
Reading state information...
Calculating upgrade...
Upgrading:
  tips-app  tips-tool

Installing dependencies:
  tips-helper  tips-lib

REMOVING:
  tips-legacy

Summary:
  Upgrading: 2, Installing: 2, Removing: 1, Not Upgrading: 0
Remv tips-legacy [1.0-1]
Inst tips-lib (1.0-1 stable [all])
Inst tips-app [1.0-1] (2.0-1 stable [all])
Inst tips-helper (1.0-1 stable [all])
Inst tips-tool [1.0-1] (2.0-1 stable [all])
Conf tips-lib (1.0-1 stable [all])
Conf tips-app (2.0-1 stable [all])
Conf tips-helper (1.0-1 stable [all])
Conf tips-tool (2.0-1 stable [all])

Nothing is held now. REMOVING is capitalised by apt because it is the part you are being asked to read, and it is the reason full-upgrade is not the default: a dependency change upstream can propose removing something you rely on, and the removal is what you have to check before answering yes.

dist-upgrade is the same command

dist-upgrade is full-upgrade under the name it had before apt got a friendlier front end. Both front ends accept both spellings, and the plan they produce is byte for byte the same:

diff <(apt-get dist-upgrade -s) <(apt-get full-upgrade -s) && echo "dist-upgrade and full-upgrade: identical"

dist-upgrade and full-upgrade: identical

The name is misleading, which is why it was replaced. dist-upgrade does not move you between Debian releases: what moves you is editing your sources to name the new suite, and dist-upgrade is then the command you run afterwards because it is the one allowed to remove things. Release channels covers that procedure.

Which to use

apt upgrade for routine updates on a stable machine, after apt update. It takes everything that can be had without removing anything, and a package it declines to upgrade is a package worth a moment's attention rather than an error.

apt full-upgrade when something has been held back and you have read why, and always as part of moving between releases. Read the REMOVING list before you answer.

apt-get upgrade in a script, and for that reason only: apt-get has a stable command line across versions where apt does not promise one, which is the distinction apt vs apt-get is about. Its stricter rule is a side effect of its age rather than a safety feature you are choosing.

Never apt full-upgrade unattended on a machine you care about. The one thing it can do that the others cannot is exactly the thing nobody wants to discover afterwards.