total solid (TS) = total dissolved solid(TDS) + total suspended solid (TSS)

any suspended particles can affect the reading of total solid but not affect on TDS

We generally consider the sample as a homogeneous medium during determination of chemical characteristics of any sample. But coming to the physical and biological characteristics, it is illogical to assume uniform presence of any material throughout the sample taken. Hence, we go for centrifuging of the sample before estimating the actual required value, since a single sample is a representation for the whole.