What is the difference between "eretz" and "sadeh" in the first chapters of Genesis ? for example Gen 2:5?
Typically, the standard glosses for these two terms work this way:
śadeh = "pasture, acreage, piece of land, landscape, territory";
ʾereṣ = "earth, ground, country, whole earth".
The links are for the pages of the Brown, Driver & Briggs, Hebrew and English Lexicon which, although quite old, is reliable for entries like these.
Applying this to the verse mentioned by OP, here it is with śadeh in BOLD and ʾereṣ in italics:
2:5 Now no shrub of the field was yet in the earth, and no plant of the field had yet sprouted, for the Lord God had not sent rain upon the earth, and there was no man to cultivate the ground.
- "shrubs" and "plants" grow in the "fields" (the arable land);
- the "earth" is inclusive of "fields" where this vegetation grows;
- cf. on the last word, "ground" (ʾădāmâ), see a previous Q&A.
Using a tool like the BibleWebApp, you can click on a word to see all occurrences of that word, which would be one reasonable way of doing your own research on the range of usage and (thus) meaning.
In addition to the previous Q&A linked under the bullet point, above, see also "Different meanings of 'Earth' in Genesis 1".
There are three words in the MT of Gen 2:5 that have meanings to related to ground,
- שדה, sadeh, field or open space (not necessarily an arable field)
- ארץ, aretz, land or the surface of the earth
- אדמה, adamah, soil, ground
The difference between שדה, sadeh, and the other two words, ארץ, aretz and אדמה, adamah is that שדה is used idiomatically, in an adjectival prepositional phrase (סמיכות כבולה), whereas aretz and adamah are used as simple nouns with their common meanings.
The word שדה has several distinct meanings in the OT, depending on its use in a verse. Besides "field", in the agricultural sense, שדה can have the meaning of rural or uninhabited places, or wilderness1. Examples of this second meaning are:
- כדב שכול בשדה, c'dov shacul b'sadeh, II Samuel 17:8 (NIV)
You know your father and his men; they are fighters, and as fierce as a wild bear robbed of her cubs.
- אשר בשדה, asher b'sadeh, Ezekiel 7:15 (NIV)
Outside is the sword; inside are plague and famine. Those in the country will die by the sword; those in the city will be devoured by famine and plague.
- וצא השדה, w'tsei hasadeh, Genesis 27:3 (NIV)
Now then, get your equipment--your quiver and bow--and go out to the open country to hunt some wild game for me.
Note that the NIV does not use "field" in any of these verses.
When used in an adjectival prepositional phrase (סמיכות כבולה), the word שדה modifies the preceding noun to give it the meaning of "wild" or "natural". This is an idiomatic usage that is common in throughout the OT and all later stages of the Hebrew language. Examples of this idiomatic use of שדה in the OT are:
- ערי השדה, are hasadeh, in I Samuel 27:5 (NIV)
Then David said to Achish, "If I have found favor in your eyes, let a place be assigned to me in one of the country towns, that I may live there. Why should your servant live in the royal city with you?"
- בהמת השדה, b'hemat hasadeh, in I Samuel 17:44 (NIV)
"Come here," he said, "and I'll give your flesh to the birds and the wild animals!"
- ועץ השדה, w'etz hasadeh, Leviticus 26:4 (NIV)
I will send you rain in its season, and the ground will yield its crops and the trees their fruit.
- חית השדה, hayat hasadeh, Genesis 2:19 (NIV)
Now the LORD God had formed out of the ground all the wild animals and all the birds in the sky. He brought them to the man to see what he would name them; and whatever the man called each living creature, that was its name.
- איש שדה, eesh sadeh, Genesis 25:27 (NIV)
The boys grew up, and Esau became a skillful hunter, a man of the open country, while Jacob was content to stay at home among the tents.
In Genesis 2:5, שדה is used twice in adjectival prepositional phrase form,
- שיח השדה, siah hasadeh, literally the "shrub[s] of the field"
- עשב השדה, esev hasadeh, literally the "grass[es] (or plant[s]) of the field"
In both of these cases, the correct meaning of the verse can only be clearly understood by translating the idiom rather than the individual words literally. The meaning is the wild plants shrubs, and not necessarily those growing on arable land. This fact is given recognition in the following translations of Genesis 2:5 that do not use "field" or other agricultural synonym:
- GOD's WORD
- Cambridge New English Bible
Regarding the other two words relating to the ground that are used with their most common meanings, the word ארץ is used twice, in adverbial preposition phrases,
- יהיה בארץ, yihiyeh ba'aretz, shrub of the field "was on the land"
- על הארץ, al ha'aretz, rained "on the earth"
The word אדמה is used once, as the direct object of לעבד, la'avod, "to work",
- ואדם אין לעבד את האדמה, "and there was no man to work the ground"
In this verse, ארץ is a general term for the surface of the earth, and אדמה is a more specific term referring to the arable soil.
The OP is a good example of how reliance on simple dictionary lookups from Jastrow, BDB and similar can lead you seriously astray in your understanding of a text.
1. The New Dictionary by Abraham Even Shoshan, Kiryat Sefer, Jerusalem 1979' entry שדה, second meaning.