Learn English – Difference between summit, apex and pinnacle

S. I. Hayakawa, Choose the Right Word: A Modern Guide to Synonyms (1968) discusses summit, apex, and pinnacle in a group of words that also includes acme, climax, peak, and zenith. Here is his treatment of the three terms you ask about:

summit, acme, apex, climax, peak, pinnacle, zenith. These words refer to the highest point of something. Summit and peak both refer most concretely to mountains; peak, however, can indicate the whole mountain or its upper part whereas summit is specifically restricted in reference to the topmost surface alone: climbing the peak to reach the summit. In metaphorical use, this distinction is lost, both words referring to the position of greatest importance, intensity, or power. Summit is the more formal of the two and has come to refer specifically to high-level conferences, as between heads of state: the settling of nuclear policy at the summit. ...

Pinnacle can refer to a turret or more commonly to a peak or its summit. It may sometimes suggest a leaner, taller silhouette than peak, however. Used metaphorically, it functions as a hyperbolic substitute for peak, often in stock combinations that approach the cliche: the pinnacle of success. ... Apex refers to the vertex of an angle, but can also indicate the tip or top of something or something at its maximum or its turning point: a battle that reached its apex the next afternoon.

Merriam-Webster's Dictionary of Synonyms (1984) discusses summit, apex, and pinnacle as part of group of words that also includes peak, climax, acme, culmination, meridian, zenith, and apogee. Here are the relevant parts of the entry:

summit, peak, pinnacle, climax, apex, acme, culmination, meridian, zenith, apogee can mean the highest point attained or attainable. Summit is applied to what represents the topmost level attainable by effort or to what is the highest in its type or kind of attainable things [examples omitted] ... Pinnacle is applied chiefly to what has reached a dizzy and , often, insecure height [examples omitted] ... Apex is applied to the highest or culminating point (as in time or accomplishment) to which everything in a career, a system of thought, or a cultural development ascends and in which everything is concentrated [examples omitted]

So the physical forms of peak (whole mountain or tip of mountain), summit (uppermost surface of hill or mountain), and pinnacle (narrow, sheer column of rock favored as a place of contemplation by the Desert Fathers after the fashion of Simeon Stylites and his pillar) differ somewhat. But used figuratively, the words blend into one another with very little sense of their distinctive underlying geological forms; and all emphasize a position at the highest possible or actual point, with perhaps (as Merriam-Webster suggests) different implications with regard to long-term stability.