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Difference between Contrast and Intensity of an Image (Matlab)

So i wanted to generate Gray Scale wedge image of 10 Levels then increase and decrease its Intensity, by high intensity means Mapping the level of gray scale image from lower value to higher values for example ,

i had a Gray Scale wedge image of 10 levels,

0   28   57   85  113  142  170  198  227  255

When i increased its intensity using imadjust the output levels are,

179  179  179  179  184  192  199  204  204  204

and here is the result in image form,

enter image description here

Similarly, for lowering the intensity i have the following results from imadjust command.

Original levels,

0   28   57   85  113  142  170  198  227  255

after lowering the intensity,

26   26   26   26   43   64   84   99   99   99


enter image description here

but what do we do in case of increasing and decreasing the contrast of an image ?

What i know about contrast is,

Contrast is defined as the separation between the darkest and brightest areas of the image. Increase contrast and you increase the separation between dark and bright, making shadows darker and highlights brighter.

Does that mean, if i want to increase the contrast of an image i should increase the high intensity levels of an image to much higher and lower intensity level to much lower ?

I am confused with contrast and the intensity as they seem opposite to each other. Kindly help me out.