See trojans and worm both are piece of malicious code or we can say programs , that harms a device or system . But there is a very basic diffrence in the mature of this programs.

And the difference is that a TROJAN is a program that enters the system or device and harms it by deleting the systems files or any other important data so you can either loose your system working or your important data .

But in the case of a worm, i would prefer to say that the nature of a worm is to replicate itself wherever it goes like if you insert a flash drive in a worm infected system. The worm will replicate itself inside the flash drive. Amd when you connect to another machine the worm will replicate itself into the new machine. But its not the work a worm do. It also sends private information of a machine or the information of user to the attacker.

Nowadays we are facing a mixture of these kind of malicious programs like we have some Ransomware which have the nature of worms and trojans as well. But to stop these things we do have a vast field of experienced experts in the market who always try to stop this kind of programs and get success almost all time .