Should I have more than one dishwashing soap? In Brazil, there is a soap paste ("sabao pastoso") commonly used to clean aluminum pots
with steel wool.  I'm guessing the benefit here, compared to normal liquid dishwasing soap,
comes only from a higher soap concentration and the pastier consistency (to keep the soap
from running downward during scrubbing).  But, the paste is black and appears more
complicated.  Is there more physics here?

And, would there be any drawback (besides cost, since you tend to use more soap when it's
more concentrated) in using this paste to clean ceramic plates with a normal sponge?

I'm not familiar with this pasty soap in the USA.  We usually use the same liquid
dishwashing soap for every surface...is this is a bad practice?
Aluminum cleaners typically contain mild/organic acids and sometimes also contain abrasives, to help remove oxidation. The black color may very well be aluminum oxide which is a cleaning abrasive (a sensible choice for an aluminum pan cleaner). A paste is also sensible for aluminum pots because these pots require a rigorous scrubbing, compared with ceramic, teflon, and steel dishware.

However, most other cleaners are neutral or basic; and other common cleaning abrasives like silicon dioxide are white. Some cleaners contain oxidizers (like peroxides) and others contain reducing agents.

Dish detergent in the USA is generally made for removing/dissolving grease. We tend to use aluminum more for disposable aluminum-foil pans, and opt for stainless steel and/or other cookware materials, because other materials are simply better quality and require less scrubbing, and/or simply diswasher-safe (unlike aluminum which tends to become blackened by the oxidizing cleaners found in dishwasher soap).