Find items that appear the same number of times in two collections
Nicely done, an efficient solution to the problem, easy to read and unit tested. For the sake of completeness, it would be good to include time and space complexity analysis. My main objections are concerning the unit testing technique and naming.

Unit testing

Each test method should have a single, clear purpose. The test methods here essentially pick 3 example inputs, but it's not clear how you picked those examples. 

In general, tests should aim to cover cases like:


Happy paths: simple execution paths that run with success
Interesting corner cases
Invalid paths: invalid, tricky, malicious inputs


All methods should have names that describe their purpose. In this particular example, it would be great to add test methods for these cases:


Should get 0 when the collections have nothing in common
Should get size if the collections have identical content
Should get 0 if either ecollection is empty
Should get size of collection if the other is superset


Btw I would use these statements as test method names, with spaces replaced with underscores.

Simplify

In the tests, instead of a List&lt;String&gt;, it would be slightly simpler to use a List&lt;Character&gt;.

Naming

Some of the names are a bit overcomplicated. I suggest some simplifications:


countItemsInCollection: as collection is already implied by the parameter type, I would drop that word from the name
compareMapForMatchingKeyAndValue: a method that starts with the name compare gives the impression that it might follow the contract of comparators, returning either of -1, 0, or 1. So it's a bit misleading. Since this method effectively calculates the intersection of map entries, I would call it intersectEntries, or even just simply intersect
mapItemToNumberOfOccurance: how about simply counts, or itemCounts