A waltz is a dance in 3/4 time. It has a heavy accent on the 1st beat, Well not accent, but stress. This makes it different to other 3/4 dances, such as the minuet and allemande, which do not have heavy 1st beats.
Prelude litterally means a lorelude to simething. they usually brief, and lead onto something. they also mainy instrumental, although there are examples of orchestral preludes etc.... such as Debussy Prelude a LApres midi d'un faune, which is an independent piece leading to nothing.
Wagener and Verdi are famous for using the term Prelude instead of overture for there operas. Prelude is mainly associated with keyboard instruments though. Earliest examples are 15th century organ manuscripts. A main feature throughout the history of the preulde is the imporisatitory manner to them. They all were immidiatly followed by something, the most popular being a fuue,a s we see in Bach. Also many composer choose this, including Shostakovich, mendelsohn, and I am sure Mozart did a few, but don;t quote me on that.
Then later on, mainly 19th century compoers, began to use the prelude alone, Hummel did a set of 24, but it was Chopin that really adopted the style. And then the preulude became a short piece exploring a particular mood, or techncal device. Many of the preuldes were composed as a hoimage to Bach, compsers such as Mendelsohn, LiszT Franck, Bussoni Hindemith etc...whereas it is siad that Rachmaninoff and Skriabin choose Chopin's prekudes as the model for theirs.
Debussy went as far as to name his, but again.. they are short, and explore a mood, or technical device, so he has held with tradition. And composers such as Poulec, Delius, and Dutilluex floowed this style of the Name,
And then people like John Cage, and other people like that composed preludes, but I havn;t looked into that beacause that sort of modern stuff don;t interest me at all.
Hope that explains it
