difference between hedge fund and CTA

What is the different between a cta and a hedge fund as the latter just mean private investment fund?

CTA is an investment strategy (also a type that must register with the CFTC, but thats a different matter). CTAs are commonly private investment vehicles, like most other hedge fund strategies.

So the similarities (CTA is considered a HF strategy, is usually structured as a HF investment, etc) are really more than the differences. Those differences can include things like the underlyings strategy (CTAs often trade futures/swaps/etc and can be in a discretionary or systematic fashion, in things such as indices, currencies, commodities, rates). Probably the most simple version is a trend-following strategy that relies on algorithms/models for signals, I find that most references to CTAs focus on this type of strategy.

The material will probably tell you that CTAs are low/negatively correlated, very liquid, and trade very deep markets…but if memory serves me they usually mean that CTAs are a type of hedge fund (like long/short, distressed, etc)

Yes, CTAs are basically managed-futures strategies (because trading commodity futures is way easier and less costly than trading actual commodities), and managed futures are generally set up as a hedge fund structure because that allows higher fees to the owners off of a lower capital base than something like a mutual fund. That is important not just because the owners are greedy (though they might be that too), but because many strategies can’t grow beyond a certain point without starting to have significant market impact from their trading. So if they are going to be small enough to stay within their capacity, but still pay out well to their owners, they need the 2/20 or 1/10 fee structure that hedge funds permit.

Technically, managed futures are a wider category than CTAs, because managed futures can include futures on financial products such as equities, equity indexes, and fixed income products, which are not technically commodities. However, some traditional CTAs have effectively morphed into managed futures because the ability to trade financial futures improves diversification and can increase sharpe ratios. For historical reasons, though, these firms may still be known as CTAs.