The 2 above are Arial, font on top, the following is Converted to Outline. They still look the same on different sizes.

The 2 bottom are my own made font. Made with Fontlab Studio 5 in TrueType format.
These image taken with screenshot, on Corel Draw.
I wonder why they look different in font and outline.

 

I would need to do testing with these to know exactly what causes the difference, but in general: that’s just the way it is. Render engines can treat outlines which are mathematically identical differently on screen depending on the way they are defined (i.e. native app PostScript curve vs. PostScript font curve or PostScript curve vs. TrueType curve and so on). I wouldn’t worry about that too much. With so many render engines around, you have no full control over how bold a font appears anyway. It will differ from app to app—or even app version to app version—anyway. 

One quick test you can do is to check how it renders in different environments. For example saving it in a PDF document and opening it in Adobe Reader and/or other apps.