The problem is not always the tools but how you use them.
Calendar needs to be one and one only and it should be personal. It contains the planning of fixed time items that has to be done at a certain time and day. Say you have a meeting on Wednesday at 2 o'clock but it takes 30 minutes to get there and it takes 10 minutes for you to pack your things then you need to allocate all the time it takes for that meeting in your calendar. So a one hour meeting maybe takes 10 minutes packing, 30 minute travel, 60 minutes meeting, 10 minutes to wrap up the meeting, 30 minutes to get back and 10 minutes to unpack, file notes and whatever.
But maybe you need to do some research, planning or other kind of work before the meeting. That you put in your todo list which contains specific things to do that are not bound to a specific time or date, like set up a telephone meeting with XYZ to discuss the new project, email ABC to get prices etc. The todo list should be organized after the type of activity/location you can do it in and not project or client.
And to make sure you have all these items done in time before the meeting, you have to put reminders in the calendar so that you can verify that it is done and if it's not, you have a second chance to do so or you may have to postpone the meeting.
You should not use the due date on the todo list. When it's due it's often too late to do it. You can use it for information but anything that need to happen on a certain date should be in the calendar. And if you need reminders to make sure you get it done in time you put those in the calendar - "check on project Z that we are on track and plan to be ready in 4 weeks". So when you look at one week in the calendar, you'll see everything that has to happen that week.
If a team work on things together you should have a worklist for that. Maybe a kanban board if it's a project or perhaps a ticketing system if that fits better. Unless everyone just works of the worklist they also need their own calendar, todo list etc. Depends on how much control they have over their work. A factory worker that works by the production line may not have to plan his work day at all.
Management of teams and management of projects are separate things compared to management of your own time.