Not a tax accountant, but:
You certainly can be both in the eyes of SARS, so long as you keep the activities separate, including trading and investing in the same shares as SARS can view the investment in the same shares as an extension of your trading strategy if they get really pedantic. Even more so for derivative products where you have exposure to the same underlying asset in both portfolios, for example a long position in your investment account appears to be a hedge against your trading activities. You'd have to be audited for this to really come to light though.
Just be sure to use mark-to-market accounting for your trading account to fully realise the tax benefits.
Remember that your investments are taxed separately upon DISPOSAL so are declared separately. While this is all good and well, it doesn't necessarily mean that CGT is beneficial over your marginal tax rate on trading. Traders can offset large portions of their tax liabilities through various mechanisms while investors simply can't. Just be careful with regards to claiming expenses in the scenario posted above - your one SSF account might not qualify you in the eyes of SARS to deduct all sorts of expenditure. Only the expenditure related to the income can be claimed and they're pretty strict on this rule with traders, in that this will be rather evident to anyone looking over your tax forms. You can certainly offset your losses though. Common occurrence with SSFs...