Is there a way to get multiple image sizes from a single image?
By default, any file you upload via the file field goes into the public files directory /sites/default/files. And you can choose to apply any image style to the same image and configure it separately per display.

E.g. Let's say you upload an image with name my_beatiful_cat.jpg from a file field on a node page.


The image by default will stay at sites/default/files/my_beatiful_cat.jpg.
From manage display of the content type, in the default view, let's say you choose the image style to be medium and save.
When you view the node, a new image will be created from the uploaded image at sites/default/files/styles/medium/public. So, you will have a file sites/default/files/styles/medium/public/my_beatiful_cat.jpg which will have the dimensions as per the image style applied.
This is true for any other image style that you apply for any other display.


So, you only upload an image once. Image styles are responsible for generating images with respective sizes as per the configuration and the appropriate image file is rendered.