I'm trying to check how many strings in column A approximately match a string in column B.
Example:
If I have the string "angry_birds_iph_app" in column B, and "angry_birds_iph_app" and "angry_birds_adrd_app" appear somewhere in column A, I would like the function to return 2.
Take a look at the Excel Fuzzy Lookup add-in. It is free to download from Microsoft. The tool implements the Levenshtein edit distance algorithm to return a similarity score between rows. Among other customizable features, the tool also allows you to set a threshold for how well the values must match in order to return the approximate result.
Rather than returning the count like you mentioned, the tool will return a table with the most similar match in column A relative to each entry in column B. From there you could simply use a filter and perform a count on the resulting column.
http://www.microsoft.com/en-us/download/details.aspx?id=15011