Are both of these sentences correct? Are there any subtle differences in the meaning conveyed?
If they are not entirely interchangeable, how do we know which one to use?
Both of them are correct, and the
和 here are the conjunction. The one
我同朋友去公园了 is also correct.
They are almost the same, but if you do want to distinguish the meanings (except for the spoken/written difference):
我跟朋友去公园了。: it seems like my friend (朋友) wanted to go to the park (公园), and s/he asked me whether I wanted to go with her/him. So I just went with her/him and left a message to my mother: "Mam, 我跟朋友去公园了".
我和朋友去公园了。: it seems like my friend and I were doing something together (e.g. having lunch), after it, we decided go to the park together.
Maybe that's not a very good example. But I cannot think of a better one because both of them are almost the same (99.9%). :p
Both 和 and 跟 mean "with." In this regard, they are basically interchangeable.
Of the two, 和 is more formal. It is also the more "equal" of the two words.
跟 has the connotation of "following" or "tagging along" in order to be "with" someone. In Chinese society, that is actually more "acceptable," because you are being "agreeable," (as opposed to "proactive"). Meaning that many would find you the companion of choice.
according to chinesegrammar.info - the most important difference between 跟 and 也:
跟 links nouns (things), 也 links verbs (actions)