Two Ways of saying the Same Thing
"your [ranger] spell save DC" and "the DC of your ranger spells" are two ways to state the same thing.
If you look at the Ranger (or other class) Spellcasting Ability:
In addition, you use your Wisdom modifier when setting the saving throw DC for a ranger spell you cast and when making an attack roll with one.
The "Spell save DC" and "Spell attack modifier" entries are just meant to record this in a simplified form.
Without good reason, you should never read a difference between the same thing stated slightly differently in 5e. There are only a few cases where doing so causes problems, and this is not one of them.
What more, this distinction would be annoying to use in actual play.
The use of "DCs" in the item description can be read to mean "ranger spell DC" and "druid spell DC", together forming 2 different DCs.
Now, while you deleted it in your paraphrasing:
you gain a bonus to spell attack rolls and the saving throw DCs of your druid and ranger spells
is different than
you gain a bonus to spell attack rolls and the saving throw DCs of your [...] ranger spells
Now, it would be perfectly mechanically valid for something to modify the DC of an individual spell while not modifying the general DC, or even (in theory) the DC of each and every individual spell while not modifying the general DC, but reading this ability as doing that is jumping through hoops and adding complications when none is needed here.
Keep it simple:
You have a ranger spell DC. Possibly you have a druid spell DC. The Sickle increases (both of) them (or one if you only have one). The ability refers back to your ranger spell DC.