For the unacquainted, running shoes and trail running shoes can look pretty similar: similar enough to think they are interchangeable and work well on both the road and the trail. In reality, both types have specific characteristics that make them perfect for the running surface they were designed for and not-so-great for others.
Take running trainers, for example. These shoes work best when used on hard, smooth surfaces, such as the road: the cushioning is fine-tuned to reduce the impact force when landing on the tarmac, and the upper is tight to keep the foot 'locked in' as you run. The 'stack height of most running shoes is also higher, especially nowadays, to improve energy returns. The outsole also tends to be smoother to increase the surface area of the shoes for better grip.
On the other hand, trail running shoes thrive on uneven surfaces. Off-road shoes have massive lugs on the outsole to claw into soft surfaces (e.g. mud, grass) and usually have an insert in the midsole to protect the feet from rocks and other unexpected obstructions (this insert is aptly named 'rock-shield'). And since the trail is more often slippery and wet than the road, trail shoes have better weather protection and are also heavier in general than road shoes.
To provide an analogue, road shoes are racing cars with their light chassis and fast ergonomics, while trail shoes are 4x4s: robust and heavy but will keep you safe in the forest. Before you buy new running shoes, consider where you will use them the most to avoid disappointment (and injuries) later on.