The role you select in the Web UI determines what you can see and do in the interface.
There are two simultaneous contexts for role usage in the web UI:
Account Context
The context selected and shown under your name in the top right of the interface affects what you can see and do in the ribbon at the top of the window. Click the drop down arrow next to your name to change the active role used in that context.
Worksheets Context
The Worksheets view provides a separate context that determines which databases and schemas you can see in the left column and what queries you can run on those database objects. Clicking on the drop down just to the top right of the query editor box will allow you to select the role, warehouses, databases, and schemas that role has access to.
Worksheet Tabs
The tabs you create in the Worksheet view are saved to your account and will be present during later web sessions. You can open worksheets saved from prior sessions by clicking the dropdown at the far right of the set of worksheet tabs shown.