Usually, trading can be considered as investing but investing cannot be called and considered as trading. When you trade that means you invest, but if you invest it's either it's a short term or long term, you need to make a choice between the time frame. In trading it depends on your position too, if you hold long position for extended timeframe, that means long term trading and on the other hand it's short term trading, like day trading and etc.
Holding are either of the two, it's either in long term and short term as well, it's the same on investing.
Back to the question, if you put it with "long term" for both holding and investing, i will call it the same, but since there's nothing, so they are not.