Again, the status of the lady and what kind of day it is will dictate whether there is any difference at all. Also, understanding the typical schedule makes a huge difference. Whether a dress is supposed to be worn during what time of day isn't really important, it's more the mentality behind it.
From my experience (which isn't a lot), there is no difference between an afternoon dress and a day dress; anyone who calls it an afternoon dress usually is referring to the fact that there may have been a reason she would have worn something different in the morning. For instance: a lady wakes up and has a good amount of housecleaning to do, including scrubbing the floor and removing all the ashes from the stove, but she's been invited later on to attend a quilting party. If she gets soot all over her dress, she would very well not wear her day dress she plans on wearing later, so she might put on a wash dress (a work dress). It probably wouldn't have been called a morning dress, because it isn't so much a dress that you wear in the morning so much as a work dress. If she was working all day long in one dress, you couldn't call it a morning dress.
An excellent, used work dress from Alabama, 1863
Later on, she might change into something more like this; the style is very conservative, but just by having specific working clothes keeps her day clothes nice.
The typical order of events in a day was get work done in the morning, and then social events in the afternoon. However, a lady who lives on a farm and does work all day long might never have the free time to do any kind of social events regularly, and likewise Mary Todd Lincoln will never ever have occasion to do any work in the morning at all.
If a lady had no work to do whatsoever in the morning and of the upper class, her before noon attire (i. e. probably not going anywhere and no one coming over), she might wear a morning dress, or a house dress. Fashion plates depict both as being excessively frivolous, although I'm guessing the reality was not nearly so. Later, during the time of afternoon she may or may not change depending on whether she plans to leave the house or expect visitors at home, although on a typical day either/or was the usual. Conclusion: a morning dress, the proper type, is not the same as the lady who woke up and had housework to do. The actual difference was like the difference between yoga pants with a sweatshirt and a little black dress with stilettos.
Another term for house dress could be a wrapper, which could have many functions for at home wear ranging from fancy silk to faded cotton to maternity wear. Women from many different social standings wore wrappers, but some were more useful and could have been worn as the most informal kind of dress. They are comparable today to a dressing robe. The main difference between a dress and a wrapper is that a wrapper typically has an adjustable waist and was meant to be worn with less undergarments (reading into that, without a corset). Some were very intricate (like the first one), and others were much less so (the one underneath is shown without a belt or drawstring, in cotton).
Isn't it funny how, when invited to someones house for dinner, or attending a party, and the invitation says 'casual', you then proceed to wear your nicest "casual"? Casual is an extensively broad term nowadays and means basically everything under the sun except black tie apparel. But the unspoken rule is that casual at home could mean your pajamas if you so chose, but going to a casual party doesn't mean your casual at home wear (yikes!). See what I'm saying? One person's casual is anothers sleepwear, and another person's everyday wear (like suit and tie to work) is anothers formal.
Back to the past.
The term promenade dress and afternoon dress are almost synonymous, in that both were the clothing that you wanted to be seen in. Using the above example, the range of acceptable was entirely personal; one ladies day dress might be someone else's evening dress, and vice versa. The words promenade and afternoon were probably replaced with the description day dress. I don't call my grungiest clothes morning clothes and then my rest of the day clothes afternoon clothes, I just spend more time in one or the other more. Also, anyone who calls their afternoon dress a day dress could be in denial that they spent time in anything less nice.
Promenade Dresses, c. 1858
A wool day dress
A printed wool challis day dress
A silk day dress, from the MET
Silk moire day dress, c. 1862-65, from Augusta Auctions
See how much of a variety there is in terms of how nice a day dress can be? The first two were more plain, but the last is far most expensive, but still a day dress.
Another way to tell the difference between a morning dress and an afternoon dress (i. e. will I be at home by myself/receiving visitors, or out walking and visiting?) is the actual structure of the garment itself. Fashion plates say that "house dresses" or "morning dresses" were very fancy. If they never left the house, they could have been made excessively nice and kept that way for years. An "afternoon dress" or "promenade dress", while still needing to be very nice, might have used some techniques to keep it nice and may have needed to be less excessive out of necessity.
Did you know that there is a difference between an evening dress and a ball dress? Let's look at the expectations between the two, and why they might be different.
If invited to a fancy dinner by the richest lady on the block, you might have several wardrobe options, depending on your income status. If your husband was on the lower end of the spectrum, then your nicest silk day dress will do, but if you are the wife of a politician then you probably have a specific dress just for such an occasion. It's cut more low than a day dress, more similarly to a ball gown, but it is saved specifically for an occasion like this. If an impromptu dance starts, there is no reason why you can't dance in whatever you are currently wearing.
A very nice day dress will do fine...
But an evening dress is even better!
Ball gown, ca. 1860 via the MET
Ball gown, ca. 1860-64, via the MET
Evening gown, 1858-59, via the MET
Evening gown, 1865-68, via the MET
-Work dress: made of either cotton or wool, depending on whether you wanted it laundered or not. Not every lady owned a grungy work dress, some needed only a less nice dress than a typical 'day dress', and some wouldn't dream of being seen in something like that.
-Wool dress: the range of when wool is appropriate is almost limitless; wool was like the jeans and t-shirt of the era, and could be dressed up or dressed down as much as needed. A plain wool could be a work dress, another one with more trim could be a day dress, and sometimes even sheer wool could be worn as an evening dress, although silk was the most desirable and appropriate.
-Silk dress: of the day dress style, with a high neckline and never with short sleeves, could be worn either as a day dress or an evening dress, or as only the very best of a lower income woman.
-Silk dress: of an evening or ball style, with a low neck and short sleeves. To decide which, take into account the color. For a ball, the lightest weight material is the most desirable, while a heavier silk was more appropriate for an evening dress.
-Sheer dress: of either sheer cotton, sheer wool or sheer silk, I wore my sheer white dress to a reenactment and was asked very bluntly, "what is it for?" Sheer dresses had many different uses, and could range from a work dress in extremely hot weather, to a day dress, also in hot weather, to being an evening or ball gown in an extravagant style. When making my own, I didn't really have an occasion in mind, but mine is definitely of the nicer day style in the summer. It has the potential to be dressed up quite a lot, and I definitely wouldn't do any work in it just because it's so white.