和 and 跟 may have the same grammatical function, when they introduce a verbal company complement, occurring before the verb. Then both are prepositions. Even more so, in the linked Zdic entries, both of them are respectively used to define the other:
In that case, they both describe together with whom the action occurs and can be used interchangeably:
我喜欢和他聊天 and 我喜欢跟他聊天
我和你说一下 and 我跟你说一下
我想和我父母去度假 and 我想跟我父母去度假
As you can see, they are used when the noun refers to a human.
That aside, 和 also works as a conjunction, as Zdic notes (连词), more specifically to coordinate nouns1. In that case, it can't be grammatically replaced with 跟：
The linked Zdic entries may appear confusing with respect to a point: I say that 跟 is interchangeable with 和 when they both are prepositions, but Zdic uses 跟 to define 和 when it's a conjunction! From the 和 entry:
The examples provided there also don't do a good job at disambiguating, as the position of the word in both 我～老师打球 and 我～老师请教 is exactly the same.
I think that's a mistake of the dictionary, because 跟 is grammatically equivalent to 和 only when used as a preposition (介词) — in that case, Zdic is more accurate, as 跟 is defined in terms of 向 and 对 just as 和 is.
My examples above show the role of 和/跟 as prepositions by placing the prepositional phrase as not contiguous to the subject of the main sentence.
1: you can't use 和 to coordinate verbs, or entire sentences