A nut (or ball) is an endpoint of a loopstring. String only have two (2) endpoints, hence, there are only two nuts.

Egglepple-wise, each nut is either a start or stop identifier (leaf).*** The two nuts of TOS are Planck data and the nanoscale, connected by Egglepple. As an arbitrary ordered pair [egg,epp], they are referred to as abscissa (toonlight) and ordinate (funshine).
/// Balls are pseudo-theoretical (abstract) objects that only exist as placement functions. There is no 'ball', so-to-speak, just a representation of an endpoint (dot). However, in gameplay, a ball can be a toy (eg. ctf flag🏁, see zero-bubble). Likewise, macroeconomically, a ball would be lyric (triangulated data point).

Mathematically, it's called a 'ball' (and sometimes 'dot') because as the string folds upon itself, the endpoints (a metric space) coordinate ("connecting the dots") into a loop, and the overall structure usually assumes a shape that is similar to some ovoid with boundary (cf., compact blob) in stereo. (see ballet, Funshine/Toonlight)