Trills and fingered/keyed tremolos are the same thing, an oscillation between two notes. If the interval is a half or whole step it is called a trill, and if the interval is larger it is called a tremolo. It is common for players to think of them all as trills, the tremolo description appears to be an academic one based upon the notation.
Trill notation is easy in tonal music with key signatures. The default is to trill to the next note in the key. But if you are in a foreign key or are not using key signatures and you want a whole step, how do you indicate it?
I have seen this notated a few ways, most often writing the trill as natural, sharp or flat, or putting the trill note in brackets. Writing the trill note is not that easy in notation programs so is not as common. I find using sharp or flat problematic as if you transpose your music with no key signatures, the required note may not be a flat, it may now be a natural or sharp.
The system I have found that negates these problems is to label it as half or whole step. This then works in any key or transposition.
A trill may be notated in the same manner as a fingered/keyed tremolo is. This can be handy if you want to start on the upper note. My rule is that if a texture contains a mix of trills and tremolos, then I use tremolo notation. If there are only half- or whole-step trills, then I use trill notation.
The exception to this is mallet percussion. As they have to play all long notes as a tremolo, oscillating between notes, passages of mixed notes should be written as diads and chords with tremolo slashes.
On stringed instruments, trills and tremolos share some technical issues with double stops and harmonics in that you are using two fingers at once. Depending on where they are, it may be hard to play legato out of a trill or tremolo into another one.
The notation of fingered/keyed tremolo can look confusing to those who are not used to reading it, as it indicates the whole duration for both notes. Unlike bowed tremolo where ties or slurs are not needed, it is important to include bowing slurs here. I have also had the odd person ask if the bow is to trem as well.
Trills and tremolos are great way to add interest to your orchestration. Depending on the notes, they can add suspenseful tension or a subtle flutter.
Sustained minor seconds are often used for tension. If I get a sketch that has a minor second tremolo, I will often add a trill to it. If I get a trill, I often add them tremolo.
If you have a three-note tremolo chord, here are a few ways you can use fingered tremolo. This can even be a good way to add interest to a sustained chord without tremolo.
In this case I have left the tremolo chords in Violin 1. If you take them out, you will be left with a soft and fluttery sound.
If you can only use one section, here is a way to make a similar sound.
To remove the sense of tension, I would lose the tremolo on the top note.