If you use graphics editing software to make an image a different size then yes, the image gets smaller and yes, the filesize of the image is reduced.
If you simply change the height/width in the html code then the file size is just as big as it was but the rendition is smaller because the parameters in the html code told it to be so.
The best thing to do for uploading/downloading is to change the size of the image with a graphics editor before uploading then upload the smaller file size. The other post just a few before this one explains more.
On the websites I do, sometimes someone will send an image to me that is 1 Meg. A 1 Meg photo takes about two full horizontal and vertical pages to display so that you have to scroll all over the screen to see the whole image. I have to reduce it down to about 50K and sometimes smaller so that it will display properly and in one window so that no scrolling is necessary to see an entire image. A good rule of thumb is to make all images that will display online be about 640X480. That's full screen on a 14" monitor with 640X480 resolution.
You just rattled my memory........ OK, if I go to where I store my graphics on my hard drive, I can open a picture with Microsoft Office Picture Manager....it says I can Resize, which I have done (but don't know if it changes the file size), and Compress. Mean anything to you. I have Windows 2000 Pro.