. We establish a relation between two different approaches to a complete pseudodifferential analysis of totally characteristic or Fuchs type operators on compact manifolds with boundary respectively conical singularities: Melrose's (overblown) b-calculus and Schulze's cone algebra. Though quite different in their definition, we show that these two pseudodifferential calculi basically contain the same operators. 1. Introduction We compare two different approaches to a pseudodifferential analysis of totally characteristic or Fuchs type operators on compact manifolds with boundary. Recall that locally differential operators in this setting are of the form x \Gammam m X k+jffj=0 a kff (x; y)(x@ x ) k @ ff y (1.1) with a kff 2 C 1 (R + \Theta R n\Gamma1 ). Here, (x; y) 2 R+ \Theta R n\Gamma1 are local coordinates near the boundary; the weight x \Gammam sometimes can be omitted. In this context, it is of interest to characterize the Fredholm operators (in an appropriate sca..