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

If there is a place or object that has been magically consecrated or desecrated within 30 feet, you are also able to locate it.

To me, it's unclear if the caster would detect some consecrated ground, then would it be possible for them to mistake it for desecrated? Or vice versa? Do they just know this ground has been touched by the gods or specifically if 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

If there is a place or object that has been magically consecrated or desecrated within 30 feet, you are also able to locate it.

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:

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. 

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.

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.}