Acrobat is showing you what is defined as the Crop Box. It does that for any page where the Crop Box is defined (like if you created a letter-size page in InDesign). If you want to see the Crop Box, Art Box, Trim Box, and Bleed Box, you can view them and manipulate them by choosing Doent > Crop Pages. If you wanted to change the Crop Box to Letter Size, click the Set to Zero button. That won't display the "trim marks" you're probably wanting to see.
To get what you probably want, go back to Illustrator, and choose Object > Crop Area > Release to get back the rectangle that defined the crop area. While it's still selected, choose Filter > Create > Crop Marks. These give you editable lines. Now export a PDF and the Crop Box will be defined as your Artboard sizeó8-1/2 x 11.