There are two "measurements" of size, and you mentioned both, but maybe have not realized the mechanics.
the "physical" or "displayed" size is in pixels... but the storage space used is in bytes.
You can have a physically large picture that does not consume many bytes (your reference to filling the monitor screen)
Likewise you can have a much smaller picture that takes a lot of storage (bytes).
In most cases there are limits for BOTH measures... Many softwares are happy to control the display size... but few let you play with the storage space directly, in JPG files, this is normally referred to a "quality" or "compression"..
I'd try irfanview (free) and when you save a picture you will see a slider for compression/file size.
Greg