Technically, there is no text shape per se. But, shapes contain a text box. When you select either of the text tools, then click on a drawing page,and start typing, Visio creates a shape without a border. The textbox tool, allows you to manipulate and move the textbox independently of the shape, but it still belongs to the shape.
It you want a single shape to have multiple text boxes, then you have to create a group, with a sub shape for each textbox.
To show/hide text, you could use multiple, stacked shapes and show hide text as necessary. Or, you could use a single shape, some shape sheet functionality, and push appropriate text into textbox.
Attached is example of 2nd method. The text is defined by the shape data values. The text selection is determined by the Actions section. The selected text is pushed into the shape via custom Field Insert formula.
Wapperdude