Learn English – “Backward” versus “backwards” — is there any difference

If you are accountable for something, you are in a position that requires you to report to or answer to someone for your actions and decisions.

If you are responsible for something, you may be the one to whom things are reported.

I think with accountability there is someone or some agency overseeing your actions; someone to whom you report.

With responsibility, you are the one in charge. "The buck stops here." One dictionary says when you are responsible, you have the ability to act without guidance or superior authority.

I am guided by the OED, which finds various meanings of distinguish, all of which are ultimately grounded in the sense of classification of things by their characteristics.

In a simple division into classes based on some, possibly unnamed, set of standards, we may say

English grammar distinguishes dependent clauses into relative, comparison, content, and complement.

Here the verb licenses the preposition into.

When the distinction is based on comparison of one class with another, we use the preposition from, noting an actual mark --

Routine violence distinguishes hockey from other sports

or by perception --

He is such a fabulist that it's hard to distinguish fact from fiction in his stories.

In the sense of separating the known from the unknown, distinguish can mean to recognize:

I saw the man from such a distance that I could not distinguish his features.

And it can have the sense of separating the remarkable from the mundane, with the reflexive or the passive:

He has distinguished himself by his scholarship.

The OP's question asks whether there's a difference between omitting and including the word from when we make the distinguishing comparison. Inclusion implies that the distinction is made by comparing things to each other; omission does not. But the difference is often slight for distinguishing a pair of things. Here's an example from a translation of Rousseau's Julie, ou la nouvelle Héloïse (Julie, Or the New Heloise): P Stewart and J Vachethat (trs) that uses both locutions in one sentence:

The pencil does not distinguish a blonde from a brunette, but the imagination that guides it must distinguish them.

Or consider this example from You Good Me Good by Jing Wang:

Some customers when buy [sic] fish they always like to ask about the female and male, actually I had no idea about how to distinguish them.

Is there any other way to determine the sex of the fish except by comparing male to female?