“peak” vs “summit”
Solution 1:
If you go by Wikipedia,
In topography, a summit is a point on a surface that is higher in elevation than all points immediately adjacent to it. Mathematically, a summit is a local maximum in elevation. The topographic terms "acme", "apex", "peak", and "zenith" are synonyms.
According to this glossary,
The summit is the highest point.
In theory, every mountain has exactly one summit. In practice, mountaineers will in many cases talk about multiple summits (eg Everest South Summit), thus blurring the distinction between "summit" and "peak".
Sometimes as you're climbing you'll approach a spot that looks like it might be the summit, only to discover it's a "false summit".
The word comes from Latin "summus", meaning "highest".
In the 19th century, "summit" was also applied to other kinds of highest points, such as the highest point reached when crossing a pass.
The same glossary has an entry for peak:
A peak is a point that's higher than all other adjacent points. In mathematical terms, it's a local maximum, the point with slope of zero along a convex-up curve. The thing to understand about this definition is that it is entirely localized: there may be some higher point not far away, but if you can't get there without going downhill first, you're standing on a peak.
In other words, most mountains will have multiple peaks.
So, to sum it all up, unless you are particular about not piquing the interest of some topographical fusspot, it appears that there's nothing wrong in using the two terms interchangeably. However, technically speaking, a mountain can have only one summit, but multiple peaks. It follows that the lone summit is also a peak :)
Solution 2:
Actually they are not the same. A peak is a point or an area that is higher than all adjacent areas So it's completely localized, meaning that a mountain can have multiple peaks ( In mathematics, it's called local maximum).
Summit refers to the highest point in a mountain. Oxford:
the highest point of a hill or mountain
and the word comes from the Latin root "summus", which means the highest. Every mountain has exactly one summit.
Having said that, most some mountaineers use these two words interchangeably.
Solution 3:
Wikipedia's “topographical summit” article says:
In topography, a summit is a point on a surface that is higher in elevation than all points immediately adjacent to it. Mathematically, a summit is a local maximum in elevation. The topographic terms "acme", "apex", "peak", and "zenith" are synonyms.
Apparently “synonyms” in that last sentence means “synonyms of summit”. However, the article goes on to use the concept of topographic prominence (“also known as autonomous height, relative height, shoulder drop ... or prime factor”) to differentiate summit from its synonyms:
The term "summit" is generally only used for a mountain peak with some significant amount of topographic prominence (height above the lowest point en route to the nearest higher peak) or topographic isolation (distance from the nearest point of higher elevation)
and then gives a few examples and lists UIAA (a climbing association) criteria used to designate independent summits.
Regarding multiple summits on one mountain, the topographic prominence article uses Everest's South Summit (ca. 8749 m altitude) and main summit (ca. 8850 m altitude) as an example in explaining why K2 (ca. 8611 m altitude) rather than South Summit is the world's second highest mountain:
While Mount Everest's South Summit ... is taller [than K2], it is a subsummit of the main summit. Only summits with a sufficient degree of prominence are regarded as independent mountains.
Solution 4:
The OED defines summit, in its topological sense, as ‘the topmost point or ridge of a mountain or hill’. For a peak it gives ‘the pointed top or summit of a mountain; a mountain or hill having a more or less pointed summit, or being conical in form.’ There is a clear difference here: peaks can be summits, but not all summits are peaks.
It would take a full search using a concordancer to establish the finer points of the distinction, but there are certainly some contexts in which they are not interchangeable. We might say ‘We’ll probably never know if Malory reached the summit of Everest’, but I don’t think we’d say ‘We’ll probably never know if Malory reached the peak of Everest’. The differences in figurative use are even greater.
Solution 5:
Most of the time they're used interchangably. Peak requires the pointy shape though, which is part of it. Summit is the very top and is not defined by a pointed shape. It just means the very top.