In D&D 5e, the detect evil and good spell states that:

For the duration, you know if there is an aberration, celestial, elemental, fey, fiend, or undead within 30 feet of you, as well as where the creature is located. Similarly, you know if there is a place or object within 30 feet of you that has been magically consecrated or desecrated.

To me, it's unclear whether, if the caster detected some consecrated ground, it would be possible for them to mistake it for desecrated? Or vice versa? Do they just know that this ground has been touched by the gods, or specifically whether there were good or evil ones?

I'm not asking with regards to a specific situation that happened in play; I'm just curious how it should go as intended by the game writers.

In the strictest RAW, it unclear, but reasonable RAI would mean a yes.

RAW

"Spells only do what they say they do."

The spell says you can locate the ground, not that you can identify it as consecrated vs desecrated. However, you could also read it as being able to locate consecrated ground, and being to locate desecrated ground, in which case the answer would be yes.

RAI

Definitely. First, what would the point of a detection spell named Detect Good and Evil be if it didn't tell you what you detected was good or evil? If you wanted to just see magic, you could use detect magic. Second, in 3.5 edition, the spell Detect Evil was actually based on alignment.

RAW: You do not know whether it is consecrated or desecrated

For the duration, you know if there is an aberration, celestial, elemental, fey, fiend, or undead within 30 feet of you, as well as where the creature is located.
Similarly, you know if there is a place or object within 30 feet of you that has been magically consecrated or desecrated.

As written, the spell does not allow for determining the difference between consecrated and desecrated only detecting the presence and location of either. All it says is: if [there is a consecrated or desecrated place within 30 feet] then [you are able to locate it].

In 5e, spells do only what they say they do and the spell does not allow any way to differentiate the two types of places, it detects both. It doesn't even say that you get to choose one to look for when you cast it. If the spell allowed you to tell the difference between the two it would say so.

The same thing applies to the first part of the spell as well.

You can't tell what precise creature type something is, only that it falls into that list and are able to locate it.

Other features have wording (which this spell does not) that specifically allows for this

Compare this to Divine Sense (the paladin ability) which specifically allows you to know the type of creatures:

Until the end of your next turn, you know the location of any celestial, fiend, or undead within 60 feet of you that is not behind total cover. You know the type (celestial, fiend, or undead) of any being whose presence you sense, but not its identity (the vampire Count Strahd von Zarovich, for instance). 

The first part of this ability is almost identical to the wording of detect good and evil, yet the ability still needs that second sentence to allow it to specifically identify the type.

See also detect poison and disease which also has the language allowing the poisons to be identified.

For the duration, you can sense the presence and location of poisons, poisonous creatures, and diseases within 30 feet of you. You also identify the kind of poison, poisonous creature, or disease in each case.

If detect good and evil was intended to work this way, it would have included a similar specification.

The spell is named poorly, but that doesn't change how it works

Some spells' names are confusing or downright deceptive¹, but that doesn't change what the spells' descriptions say they do. In this case for example, detect good and evil doesn't detect alignment at all, but it senses creature types often associated with some alignments as well as objects and places that have been touched by divine power. Other than that it does do what it says: detect. The spell detects all of these things and allows them to be located. Nothing in the spell indicates or even implies that you can differentiate between the things that are found.

Rules as Fun: Harmless to allow as a houserule

Besides potentially stepping on the toes of the paladin feature Divine Sense, there really is nothing that would break by allowing the caster to know the type of creature or if ground was consecrated or desecrated. It would be a small boost in utility, but certainly nothing to be super concerned about. We play it this way at my table and have had no issues.

If your campaign plot is full of fiends pretending to be celestials (for example) or your plot is fragile to such abilities obviously you should see caution in adopting it.

Just note that this would be a houserule so not really allowable at Adventurers League tables or other tables that strictly adhere to RAW.

^{1 - A few examples: Catnap, does not put creatures to sleep. Sacred flame does not do fire damage. Chill touch does not do cold damage and is also not a touch spell. Daylight does not actually create sunlight.}

You can't tell the difference because there is no (mechanical) difference

In order to answer this question, we have to ask exactly what "consecrated" and "desecrated" mean in terms of game mechanics. The only place I can find any explanation is in the Paladin's Divine Sense:

Within the same radius, you also detect the presence of any place or object that has been consecrated or desecrated, as with the hallow spell.

From this, it seems that the hallow spell is the way to consecrate or desecrate something. So, what does the spell's text have to say about consecration and desecration? Well... nothing. At least, not directly. But depending on the parameters you choose when casting hallow, you could have an area that protects all within it from being frightened and does not allow undead or fiends to enter. That sounds a lot like consecration. Or you could have an area that causes vulnerability to necrotic damage and prevents celestials from entering. This sounds a lot like desecration.

The point is that in practice, both consecrated and desecrated ground mean the same thing: that someone cast a hallow spell there. Whether the hallowed area is consecrated or desecrated is merely a matter of opinion with no mechanical import. Hence, detect evil and good can't discern any difference between the two because there is no difference to be discerned. The person who cast the hallow spell would most likely say they had consecrated the area, while a cleric of an opposing faith would accuse them of desecrating it. This lack of explicit distinction between consecration and desecration is consistent with the overall downplaying of alignment-based mechanics in 5th Edition (e.g. the fact that detect evil and good detects creature types rather than alignments).

Of course, the DM of a campaign is free to invent other ways to consecrate or desecrate an area besides the hallow spell, and they are free to consider consecration and desecration as distinct states within their game world. If they do decide to make a mechanical distinction between the two, it would also make sense for them to rule that detect evil and good (as well as a Paladin's Divine Sense and other similar abilities) can detect the difference. Even if the DM does not make any objective distinction, it would not be unreasonable to rule that when you detect hallowed ground, you get a sense of your deity's subjective opinion on whether it is consecrated or desecrated.