Hello, I was wondering what the different types of accounting professions are associated with a commercial business? Can you please name the different specific titles of the professions

that is an interesting question John. There is no specific "commercial accounting" designation, so you will find that there are CA's in public practice, industry, small business, government and education. Same applies for CPA. The things that probably set public practice apart from commercial business accounting is the type of work you do lends to different specialisations.......which involves perhaps post-grad diploma or specialist courses that help the accountant in their chosen field.
One thing you can take to the bank is that of all the accounting designations, you will find some that require a significant amount of post-graduate training and further education. And some are for want of a better word a "membership" that requires next to no effort to join, as long as you have the fees.
SO if you are looking to employ someone internally in your business, go with someone with a recognised qualification such as CA or CPA....they had to work pretty hard to get their ticket. Ask them how much time they had to work to get their qualifications, and what areas of accounting they covered in getting there.
If you are looking for guidance in career choice for yourself, go with the hardest qualification to obtain: it will carry the most weight when applying for jobs.
Hope this helps
regards
Brendan