The only similarity I can see is that both requires some initial funds.

Investing is more or less limited to just one direction: a growing market. Buying the asset to sell it later at higher price.
However investing in PoS coins can be profitable within some small price drop as well (because due to staking you will probably own more units of the asset than you originally bought)

But trading offers two ways to make profit as margin trading allows you to "sell" stuff you don't even own (had bought) so you can make profit on price dropping asset as well.

I would say the main difference is that active trading requires constant oversight (either manual or using scripts, bots etc.) and changing/updating positions to maximize the profits (or cut loses) while investing is more about few buy actions and waiting for good sell opportunity.

sum up:
Investing => targeting only continuously growing assets (or assets you believe is going to grow in future )
Trading => asset itself is no so much important, it's more about watching it's market behavior ( price fluctuation, volume ) and your reactions.