To the first part of your question: No, I don't believe so.
To the second part of your question: Yes, I believe you can be classified as an "investor" for shares, whilst also being a "trader" for CFDs in the same year.
My understanding is that it's not necessarily a blanket classification attached to the taxpayer per se, but rather a classification of the specific activities associated with the different financial instruments that the taxpayer might be active in.
To summarize and hopefully make it a bit clearer, let's use an individual taxpayer (not unlike yourself) as an example, who is neither a recreational gambler (for CFD purposes), nor a full-time professional "trader". But in all cases we will assume that the taxpayer is approaching their market-related activities with a financial profit/gain-making motivation. Let's say that our taxpayer conducts various buying/selling activities across a range of different financial instruments within a given tax year. In very general terms, the ATO would most likely classify/treat those various activities as follows:
1) Shares: Investing - on capital account (very clearly financial assets).
2) CFDs: Trading - on income account (because they are not assets per se (in this example), but financial contracts).
3) Futures: Trading - on income account (also because they are not assets per se (in this example), but financial contracts).
4) Options: I cannot say with any degree of certainty because I have never delved into them, but I would think that it would/might be heavily dependent on whether those options were exercised or not. Keeping it simple, assuming no exercisings, I would think they would be treated as "trading" (i.e. profit/loss - income account) because they too relate to financial contracts (i.e. similar treatment to Futures and CFDs), rather than acquiring/disposing of assets (shares).
I'd speculate that the above example is probably a fairly unlikely scenario (i.e. that our punter periodically operates across all these markets within the same tax year), but it hopefully demonstrates that the ATO is capable of (and does) treat the various activities separately - assuming, of course, that our punter has not crossed a line in which The Commissioner would consider him/her to be a "trader".
Naturally, all the usual disclaimers apply about seeking independent profession advice that is specific to your personal circumstances. That said, I hope I have explained it reasonably clearly.
Cheers,
Z
(*For the purposes of this reply, and to avoid any ambiguity, I have been careful to only use the word "trading" in the context of being classified as a "trader" for a given activity. That's why I used the rather cumbersome "buy/sell" language. In reality, we often use the term "trade" with slightly different meanings, depending on the context, but I didn't want to introduce any confusion here.)
