I shall deal almost entirely with symbolic AI in my lectures.
The name ``symbolic AI'' is usually opposed to ``connectionist'' AI, also known as PDP or neural nets. However, terminology differs between authors.
For example, according to Chandrasekaran, Fodor and Pylyshyn talk about ``classical'' models, Dennett uses the term ``High Church Computationalism'', and so on. But the term ``classical AI'' is not well-defined either. Some authors use it to refer to ``symbolic AI'' combined with assumptions about the need for explicit representation of world-models, goals, and such entitities. See page 45 in Intelligence as Information Processing, in Foundations of Artificial Intelligence edited by Partridge and Wilks (PSY KH:P 025). This article analyses the difference between various AI paradigms, and between differences in terminology. I recommend reading it, preferably after you've seen examples of both symbolic AI and connectionism.
So if you use such terms, define what you mean! Strictly, ``symbolic AI'' is a misnomer, because connectionist systems also symbolise things. It would be better to say ``AI as computation over discrete symbol systems''. I shall explain why in the following section. However, for brevity, I'll stick to the term ``symbolic AI''.