What is trace-based seismic Inversion
I too have found this nomenclature rather confusing.  I am pretty sure that trace-based inversion is merely where each seismic trace is inverted independently of surrounding traces. This would take into account most deterministic/probabilistic inversion types (e.g. model, coloured, sparse, etc). In contrast, geostatistical inversion would not strictly be trace-based inversion, as it uses a spatial and temporal variogram to takes into account the expected results of surrounding traces during the inversion, even though it does invert on a trace-by-trace basis. Confusing. 

The following paper describes trace and geostatistical inversion methods:
Germán Merletti, and Julio Hlebszevitsch. 2003. Geostatistical Inversion for the Lateral Delineation of Thin Layer Hydrocarbon Reservoirs: A Case Study in San Jorge Basin, Argentina. SEG 2003. 

I've found the following paper very useful for understanding seismic inversion (geostatistical isn't discussed, though): 
Dennis Cooke and John Cant. 2010. Model-based Seismic Inversion: Comparing deterministic and probabilistic approaches. CSEG Recorder, Vol. 35, No. 4.