All the distances measured by my computer are smaller than when I measure by real ruler. This is true for any programs which has ruler. When I go to iRuler.net, the monitor dimension it distinguishes is 16.3'', while the one printed on the manufacturing label is 14'' (the dimension that fits my ruler is 13.9''). My screen resolution is 1366×768 as recommended. Do you have any explanation for this?
There may be several different things going on. First manufacturer specs for screen size are based on a diagonal measurement and may include what is hidden behind the plastic bezel. So that's not a particularly useful measurement for your purposes. If the manufacturer published a 14" spec for the width, that probably represents the nominal dimension of what is behind the bezel.
A common pixel resolution for monitors is around 96 ppi, so 13.9" for 1366 pixels is about right.
There are two types on on-screen rulers. One type displays the physical size of what is displayed on the screen (which requires input of the monitor pixel density for accuracy unless it is reporting pixels). The other is used within an application to display the output dimension when the "document" is printed. That won't necessarily match anything in real life if you compare the screen display during editing to a ruler.
The iRuler.net ruler is based on a typical screen density and typical bezel losses. The web site can retrieve the resolution of your monitor but not the actual hardware identification or screen density. It guesses the screen size. If the ruler is not accurate or it displays the wrong screen size, click on the "select your monitor dimension" link and select the closest size that matches your screen (diagonal measurement). That should produce a pretty accurate ruler.