What are the implications of a nonparametric machine learning algorithm?

Question

I've been looking into the advantages of using a Random Forest classifier and stumbled upon this

random forests are non-parametric

Looking at the definition of what non-parametric statistics mean, I found this on Wikipedia:

1. The first meaning of nonparametric covers techniques that do not rely on data belonging to any particular parametric family of probability distributions.
2. The second meaning of non-parametric covers techniques that do not assume that the structure of a model is fixed

I'm trying to understand what that means in the context of supervised learning, but I'm left with several questions:

For the first point, does that mean there is no assumption about my features coming from a certain set of distributions or my labels or both? Does it also imply that I don't assume any relationship between features and labels (e.g. linear, polynomial)? What else is implied?

Also, I do not quite understand the second meaning of non-parametric and would be happy about an example or more intuitive explanation.

Answer 1

For the first point, does that mean there is no assumption about my features coming from a certain set of distributions or my labels or both? Does it also imply that I don't assume any relationship between features and labels (e.g. linear, polynomial)? What else is implied?

I think both features and labels are not coming from a certain set of distributions, and I think the relationship can also not be fixed which reflects the second meaning.