Have you ever worked in finance before?
I have not but the exact definition is the field that deals with the study of investments, I find a lot of it to be so confusing but some people eat it up like peanutbutter!
I know, some many different terms, that I do not understand, do they have a name for people that study this or work in the field of fiances?
It really depends on the field, there are three sub categories that finance can be broken into, public finance, corporate finance, and personal finance. I imagine each subcategory has a different name and companies may have different financial needs and some special titles. 
I see, it really does have a lot to it. What exactly is public finance?
Public finance
Public finance is the study of the role of the government in the economy. It is the branch of economics which assesses the government revenue and government expenditure of the public authorities and the adjustment of one or the other to achieve desirable effects and avoid undesirable ones.
The purview of public finance is considered to be threefold: governmental effects on (1) efficient allocation of resources, (2) distribution of income, and (3) macroeconomic stabilization.
Overview.
The proper role of government provides
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