Why when I save a photo it displays a different date then the actual date I saved it
The date and time in question doesn't usually refer to the last time it was edited or saved. Typically, it'll refer to the date and time the photo or screenshot was originally saved (i.e. originally taken).

Obviously I can't comment on the photo in your question, but my guess is that the time of 3:29pm and date of 23 March 2005 is what's in the metadata of the photo, and that it was originally taken by a digital camera of some sort at that time (obviously not with your iPhone).

Any photo taken with an iPhone (or any digital camera) will actually also store a whole heap of metadata. In addition to the date and time it was taken, it can capture the colour mode, size in pixels, depth, and so much more. When you then edit that photo with your iPhone (or digital camera) it'll also capture the date and time it was modified.

However, in the Photos app of your iPhone the metadata it'll display is the date and time the you took the photo (or the data and time it was originally taken by whichever digital camera it was). 

Editing the photo doesn't change the metadata being displayed, not even if you opt to use the Copy or Duplicate options.