Summit and peak can both be used as nouns, adjectives, and verbs with or without objects. Several dictionaries list them as a synonym for each other, especially when talking about a mountain. There is a subtle difference however. The summit of a mountain is the highest point whereas the peak is the pointed top of a mountain. So, the summit is a peak, but there can also be other peaks nearby the summit.
Also both words have other meanings. For example, summits between Trump and Kim Jong Un and Trump and Vladimir Putin have been in the news a lot (2018). In this context, summit means a meeting with the highest level of government officials. Peak can also be used to describe someone as sickly.
According to technical terms as mentioned in most dictionaries, a peak is a top of a mountain that is pointed. Usually, all mountains tend to have a number of peaks. However, a peak does not necessarily have to be the highest point of the mountain. For this, the term summit is used. It is a word that coes form the Latin word ‘summus’ which means ‘highest’. Technically, summit is the highest point of anything, especially a mountain.
Although, in common usage, both the terms peak and summit are used interchangeably without much differentiation. Technically speaking, however, there is a big difference in both the terms as mentioned earlier