What does a trilogy need that a series doesn’t? A trilogy must have a real and viable connection within the three books. Either the same main characters throughout the three or secondary characters from the first book taking on major roles in the second and third books.
Or a single goal throughout the three books, such as a problem needing to be solved, which finally is taken care of in the third. Or a specific setting that’s the core of the trilogy. Or a family connection, where various members may encounter different settings, but the people in the trilogy are all related.
In my Darkness of Dragons Trilogy, the books are connected by the same house and area (setting). And by the goal, which is essentially the same in all three--to control the Black Dragon.
On the other hand, In my Dagon House Ghosts Trilogy, the connection is simply the house (setting) and what happens to the people who are staying there. That and the ghosts.
On the other hand, a series needs only to be loosely connected in some way. That to me is the difference.
Again, the connection can be a family, such as in my Golden Chances Series. Or a setting, which that series has as well.
In my Temple Of Time Series, the series title is the connecting factor, because once you enter this place, anything can happen.
Also in a series, years can pass between the books.