What is difference between aggregate functions: count and cumulative count?

The count is well known and is simple to explain. Count function counts a number of items/records that satisfy the given criteria.

The cumulative count function is the sum of all the counts generated so far. Mathematically it is represented as

Sk = ∑Ci for i = 1 to k

When k = 3, i.e., 3rd cumulative count is calculated by adding up the first 3 counts C1, C2, C3

This might seem not very clear. So let's clear the air with an example:

Consider the following table:

The above table is generated by using a simple count of specimens collected every day for the first 5 days of the month of Jan 2018. However, this table doesn't give an idea of how many specimens were collected in total until a given date. For this purpose, we need to use a cumulative count. The 3rd column in the below table is generated using the cumulative count function.

The difference can be best visualized using below the graph.