As an exercise in writing bash scripts and using recursion I created a script to count the number of files and directories in my home directory. To check the result of my script I ran find -type f | wc -l and find -type d | wc -l to compare the count of files and directories. The results from the find runs differed from my scripts results. So after allowing for links and hidden files I still had a discrepancy.
The results of find -type f when run on an empty directory returns no file names and a wc count of 0, but when find -type d is run on an empty directory it returns the name of the directory giving wc a count of 1.
Is an answer of 0 or 1 the correct response for an empty directory?

What do you mean by correct response?

To me, find's output is not surprising. The directory is not a regular file, thus nothing is printed when using -type f. It's a directory, thus its name is printed when using -type d.

I will try expressing this a different way. As I read the manual the command find enquiry_dir -type d should tell me how many directories are in enquiry_dir.
So I run this code
col@nyloc:~$
col@nyloc:~$ mkdir testdir
col@nyloc:~$ mkdir testdir/emptydir
col@nyloc:~$ find testdir/emptydir/ -type f
col@nyloc:~$ find testdir/emptydir/ -type b
col@nyloc:~$ find testdir/emptydir/ -type c
col@nyloc:~$ find testdir/emptydir/ -type p
col@nyloc:~$ find testdir/emptydir/ -type l
col@nyloc:~$ find testdir/emptydir/ -type s
col@nyloc:~$ find testdir/emptydir/ -type d
testdir/emptydir/
col@nyloc:~$ ls testdir/emptydir/
col@nyloc:~$ ls testdir/
emptydir/
col@nyloc:~$

Why does the test for how many directories are in an empty directory not come back with null as all the other tests do?

I don't see this stated in the man page. As far as I understand it, find also processes the root of the directory tree, that is enquiry_dir itself.

However the -empty option may help:

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I must need a new book on Linux then.
From Linux in a Nutshel written by Jessica Perry Hekman published by O'Reilly Copyright 1997

find
-type c
Find files who type is c. c can be b, c, d, p, l, s, or f.

there are no files of type d in emptydir in the above example.

There are no files in emptydir, but emptydir itself is a directory, and therefore printed. Find doesn't operate on files in a directory, but all files in a directory subtree, including the root of that subtree.

If you want find not to include the command line argument itself in its outut, use the "-mindepth 1" option:That should give a list of all directories under the current working directory (the CWD is the implied argument in the absence of any other path arguments), but not list the CWD itself.