The problem these solve
Most productivity software assumes the hard part is remembering what to do. For most people it is not. The list already exists - in a task manager, a notebook, a Slack thread, a manager's head. The hard part is that the list keeps offering itself for reconsideration, and every reconsideration costs a few minutes plus the attention needed to get back in.
Both apps in this category attack the same moment: the one where you look up, having finished something, and have to decide again.
How to choose between them
Anchored is for people who work from a plan. You pick one anchor task for the day, give it a duration like "45m", and it sits in the menu bar with a live countdown while the rest of the queue waits behind it. When the timer ends you get a notification with a one-tap Done or a snooze. It is keyboard-first, with a quick-add box and rebindable hotkeys, and it can roll unfinished work to tomorrow instead of letting it rot at the bottom of a list.
CatPod is for people who work better with a nudge that is not a nag. It puts a pixel cat on your desktop with a pomodoro timer attached. The cat wanders around, reacts to your cursor, and marks the end of a session. It sounds frivolous and it is - deliberately. A timer you enjoy looking at is a timer you keep using, and the sessions are the same 15/25/50 minute blocks you would set anywhere else.
If you want a plan enforced, take Anchored. If you want the day paced without being managed, take CatPod. They do not conflict, and some people run both.
What neither of them does
Neither app syncs, shares, assigns or reports. There is no team view, no integration with a project tool, and no analytics dashboard telling you how productive you were. If you need any of those, these are the wrong tools and a hosted service is the right one.
What you get instead is an app that opens in under a second, works on a plane, costs nothing if you want it to, and does not have an opinion about your workflow beyond "decide once, then look at the decision."