Some circular slide rules seem to be a familar linear rule in circular formfactor. They have nonrotating part (stator), rotating part (slide), cursor. Stator and slide carry familiar C/D scales, sometimes A, B, K, S, T, L ... etc. Such slide rules have certain advantages and disadvantages comparing to their linear brethren.
Advantages include "closed" log scales, which eliminates the necessity to reset the slide, compact design and ease of making at home (you just need to print faces on your laser or jet printer, cut them out and join them with lapel pin in the middle).
The disadvantage is that scales close to center become really congested. Also it seems that it takes more time to perform basic operations.
While being somewhat similar mechanically, astrolabes have very different mathemtical foundations. They are based on properties of stereographic projection (other projections were also used) rather than logarithmic scale.
Astrolabes have history that spans several centuries (possibly, millenias) before slide rules. There is little doubt that William Oughtred based his slide rule design on astrolabe.