New answers tagged date-time
If I understood you correct you want to set your date as yesterday, two days ago, etc. and not just to see actual date 18.08.2015. If so, there is choice field when creating date column, name of that field is Display Format. you should choose Friendly option, default option is Standard. I do apologize if you meant something different to ask.
The formatting is done server-side, you would have to replicate it (and and the Today difference calculation) either in a Calculated Column or with CSR - Client Side Rendering This StackOverflow post explains why/how: How to use Today and Me in Calculated column
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