The class of problems for which a 1-1/poly(n) fraction of instances are solvable by a BPTIME(f(n)) machine. Thus, HeurBPTIME(f(n)) has the same relationship with BPTIME as HeurDTIME.
Thus HeurBPP is the union of HeurBPTIME(nc) over all c.
The class of problems for which a 1-1/poly(n) fraction of instances are solvable by a BPP machine.
[FS04] showed a strict hierarchy theorem for HeurBPP; thus, HeurBPP does not equal HeurBPTIME(nc) for any fixed c.