For people that use Windows especially, Microsoft's approach to Teams has been a bit of a mess. Windows comes preinstalled with Teams, but this version doesn't support work accounts. For that, you need to install a different app also called Teams.
This is finally being resolved. Sometime within the next month, Microsoft is planning on rolling out a single "Unified" version of Teams. This will support both work and personal accounts, and allow you to switch between them if you have both. It is also possible to split the account into two different windows so personal and work chats are kept separate.
In future versions, the app will also allow you to pick which account to join any given meeting with, or even to join without signing in at all. It will also include some improvements to notifications.
If you are currently using the "Teams (Free)" version that did come with Windows, you will need to move to this unified version, as the other version will ultimately be forcibly removed from machines eventually. However, that is a small price to pay to remove a major source of confusion for users. Most business users will already be using the correct version, so will not need to make any changes.