These 2 terms are often used interchangeably. The problem is that there is no set definition for image resizing which can create some unexpected surprises.

When I produced files for printing, we made a couple of “house rules”:
1. When someone requested that an image be resized, the resolution of the image was not changed.
2. When resampling an image, however, the resolution of the image would change.

Ben Bounketh’s blog on DPI and Resolution explained how resolution is a fixed amount of pixels in an image. Refer to his comment, "If I said 'this 100 DPI image has a resolution of 300 x 300 pixels' you would know that it is a 3" x 3" image." We'll go a step further now and resize the 3" x 3" image, which is its bounding box, to 1” x 1” a 1/3 reduction. Since we did not change or lose any image data this 1” x 1” image still has the same amount of resolution, but since it is 1/3 smaller, all of those pixels are now packed together 3 times closer and the is image is now 300 dpi.

Let's say I want to use the image as a 1" x 1" thumbnail; the resized version of the image is still the same file size as the 3" x 3" file—about 300K uncompressed.  That would be a very large file to download as a thumbnail, especially if there are a lot of thumbnails on the page.  And, if the browser doesn’t recognize my 1" x 1" bounding box, I’ll probably have text reflow around the 3" x 3" image as it re-adjusts to a display resolution.

The solution is to resample the 3" x 3" image as it is resized to 1" x 1". In Photoshop menu Image select "Image Size" and have "Constrain Proportions" and "Resample Image" selected. Input your new size requirements and select OK.

Notice that with the new size and resampling, the "Pixel Dimensions" file size is significantly smaller and more inline with what you would want to use as a thumbnail image.

One reason why this is important is that many photo sites that store images will tell you that they will resize them for you. If you are storing your original images on one of these sites you could find your beautiful high resolution photos have been resized and resampled to a size that no longer looks good for printing or blowing up on your web page.