MacOS – Choosing native screen resolution aspect ratio when screen sharing

The supported resolutions defined on the Apple pages are for the built-in screen which is, pardon the pun, comparing apples to oranges in this case.

Plugging an external monitor in will show those resolutions that the monitor supports and you will be able to achieve the maximum resolution of the Dell monitor which is 1600x900

It depends of what you mean by "will look the same".

It looks the same only in the way that the elements on your screen are displayed in the same size as if it was a 1280x800 screen.
The aim of the retina displays is to display more details, to do that, what it does is that it displays things at the same size a half resolution screen would have done but uses all the available pixels to show you more details, nothing is better than an example to explain you what I mean :

In fact, the pixels of a retina display are designed to be small enough so that you retina won't be able to distinguish them at a standard use distance, that's why it looks as sharp as a printed page, and that's why a retina display will never look the same as a display that would be natively 1280x800 pixels, actually it should looks much better.

Now let's answer to your question ! You didn't explained if it always looks blurry or only on some applications/websites.
I will assume that it does not always looks blurry because it shouldn't.
As I explained, although they are displayed in the same size than on any other display, the elements are "constituted" of 4 times more pixels which means that an element that would have been 10x10 pixels (100 pixels) needs to be 20x20 pixels (400 pixels) to take advantage of all the available pixels ; it looks blurry if the element hasn't got a resolution that's high enough "to fill all the available pixels", in fact, this is exactly like when a picture is pixelated but here it looks more blurry because the pixels of your screen are extremely small.

There should be more and more retina ready websites/applications in the future (in think that in something like 4 years most of the websites will be).