Hi Kelemvor333. Yes, a plan created in Planner is seperate from a plan created in Microsoft Teams. When you create a new plan in Planner, it will create an Office 365 group. The Group will be using Outlook as the default Conversation experience - i.e. an Outlook group, rather than a Microsoft Team or a Yammer group. Any comments you make on tasks within a plan will be reflected in the Outlook group conversations.
When you create a Microsoft Team, it is also creating a new Office 365 group. Any plans you create in the channels of the Team are associated with the Team and it's channel. But they wont appear in the Planner website.
However, while creating a new Microsoft Team, you can repurpose an Outlook group and it's plan, attaching it to the new Team.
As you create your Team, you have an option to "add Microsoft Teams to an existing Office 365 group." That is, if you're an owner of an Office 365 group.
You can choose the group created when you created the plan. Once the Team is created using that group, you can add a tab for a plan and choose the existing plan.
Dave Heller covers the process in more detail, with video, in the following post. Bringing a Plan into Microsoft Teams.