That does help a lot. I note that the part of the slide that is imaged with the OpenFlexure Microscope has more clustering of the red blood cells, which makes the images look more different and the white blood cells less obvious, but I think we can see all of the effects. We can compare these images also with the one from the website in post 16, which @JohemianKnapsody identifies as being taken with a 100x oil immersion objective and Giemsa stained (post 18). There is also your earlier image in post 6 of this thread.
Looking at apparent magnification first. The OpenFlexure imaging optics is designed to use as much of the image circle of the objective as possible, but to avoid vignetting. In the design we assume that the image circle (called the field number) is 17mm. As the camera sensor is rectangular this cannot take the whole of the round field of view. Many modern microscopes are designed with a wider field of view. Taken together this means that the field of view of the OpenFlexure optics is usually smaller than for a microscope using eyepieces. However, your image from your laboratory microscope above is also a camera image. It will also have a relay lens to match to a particular camera sensor size. Usually microscope manufacturers offer a range of relay lenses for 2/3", 1/2" etc sensors. Different combinations of relay lens and camera will give different field of view (apparent magnification). Your OpenFlexure Microscope example image in post 6 (40x air objective) and the website one in post 16 (100x oil objective) both have the cells are reasonably spaced. Roughly counting cells, the 100x image is about 20 cells across, and 20 cells gets about 40% of the way across the 40x image. This is as expected. The images above from your laboratory microscope are somewhere in between, it looks as though you have a relatively small sensor camera, which is cropping out the centre of the image circle of the 40x lens.
Do you get a similar field of view with your laboratory microscope if you use the eyepieces instead of the camera? Are the eyepieces the standard 10x, or are they 15x or 20x?
Colour. Your two images above from the OpenFlexure Microscope show quite clearly the colour saturation falling off away from the centre of the image. Overall then the image appears to be lacking colour. If I take a crop from the centre of the image, then you can see that the colour of the cells and the differentiation between red and white cells is much more like the images from your laboratory microscope.
The red cells are not well defined because they appear to be clustered in this region of the sample, but the two white cells are clear from the colour of the nucleus. There is less overall pink bleeding into the background in this image than in the ones from the laboratory Microscope.
This indicates that the colour correction is working as expected. It also shows that the known issue of colour mixing at the edge of images that arises from using a Pi Camera v2 in the microscope is quite prominent in this application.
Finally, to answer your direct question of how do you get an image similar to the one in post 16? This higher resolution image was taken using a 100x oil immersion objective. The cells are much more well defined than in the images from your laboratory microscope, which is to be expected as the NA of the oil immersion objective is probably twice the NA of your 40x lens. An oil immersion lens (used with immersion oil) in either of your microscopes will improve the resolution, but to get the full performance you will additionally need to pay attention to the focusing of the illumination. The final observed image resolution is a combination of the NA of the illumination and the NA of the objective lens. The image in post 16 will have had careful alignment of the illumination. Comparing the colour of your images from your laboratory microscope with the image in post 16, it looks as though the depth of colour in the staining on your slides is not as deep as the slide that @JohemianKnapsody used. It is a little hard to tell, because there are no white cells in that sample. The apparent colour is also enhanced by the higher resolution giving a clearer differentiation between the cells and the background. However, even in that image if you look closely the cells in the centre are pink, but the cells at the edge have not got much colour. The higher resolution gives better light/dark contrast which helps to differentiate things by contrast and morphology and slightly masks the effect of the reduced colour saturation. Differentiating between cell types (or morphology of the different red cells in post 16) is also helped by the sparser cell distribution during slide preparation.
A slightly different question would be: How do you get a field of view similar to your laboratory microscope? There are three ways to do that - crop the images, use a longer focal length tube lens in the optics module, or use a higher magnification objective. The first two just zoom in to the image, they will not give any more detail, but I think that is what your laboratory microscope is doing anyway. Cropping the images will give a remedy to the colour saturation, but would require software modification to do in the live view. A different tube lens or a different objective would give the smaller field of view in the live stream, but would leave the colour saturation problem. A higher NA, high magnification objective could give better resolution, which might mitigate the lack of colour around the edges.
A final version of the question would be: How can we solve the colour saturation problem? If you follow the method in Flat-Field and Colour Correction for the Raspberry Pi Camera Module | Journal of Open Hardware then it is possible to retrieve more colour around the edges. You would need to do that in post-processing.
The software team are working on solutions to the colouration in the live view, either by applying the unmixing, or by implementing different hardware. While both appear to give really good improvements, the software is very much in development. It is missing many necessary features and is not yet ready for wide use.
