Wikipedia to the rescue!

> jelly (from the French gelée)[29] is a clear or translucent fruit spread made by a process similar to that used for making jam, with the additional step of filtering out the fruit pulp after the initial cooking.

https://en.m.wikipedia.org/wiki/Fruit_preserves#Jelly

That seems entirely counterproductive. Why remove the fruit from jam?

Berries with seeds are strained to remove the seeds. It tastes nice so we do it with everything else too.

Jelly is thickened juice, jam contains the pulp. Why? Different textures.

When making them we (UK) tend to use pectin as the thickening agent for jams/marmalades and gelatin for jelly. You can buy sugar with pectin added marketed as 'jam sugar'.

Jam should be nowhere near as firm as jelly.

And does agar based jelly count, or just gelatine?