The difference between subsume and consume

is that "subsume" is to place under another as belonging to it; to include or contain something else and "consume" is to use up.

subsume

To place (any one cognition) under another as belonging to it; to include or contain something else.
To consider an occurrence as part of a principle or rule; to colligate

A few years later , he and I joined forces to publish an even more powerful theorem which subsumed almost all the work in this area that had gone before.
no allusion is made to forms because Plato is subsuming under the class of productive crafts both divine and human imitation;

(transitive) To use up.
(transitive) To eat.
(transitive) To completely occupy the thoughts or attention of.
(transitive) To destroy completely.
(intransitive, obsolete) To waste away slowly.
(economics, transitive, intransitive) To trade money for good or services as an individual.
(transitive) To absorb information, especially through the mass media.

(use): burn (of energy), use, use up
(eat): devour, eat, swallow
(occupy): occupy, overcome, take over
(destroy): annihilate, destroy, devastate, eliminate, obliterate, raze (of a building), wipe out

The power plant consumes 30 tons of coal per hour.
Baby birds consume their own weight in food each day.
Desire consumed him.
The building was consumed by fire.
If he were putting to my house the brand / That shall consume it.
Lay not up for yourselves treasures upon the earth, where moth and rust consume, and where thieves break through and steal: but lay up for yourselves treasures in heaven, where neither moth nor rust doth consume, and where thieves do not break through to steal: […]
Therefore, let Benedick, like cover’d fire, / Consume away in sighs.
But, sir, you see how weak I am. You must see that I have been consuming from day to day […] .
He assured her the child was consuming at that moment in the next room.
In a materialistic society, individuals are taught to consume, consume, consume.
If you consume this product while in Japan, you may be subject to consumption tax.
The Internet has changed the way we consume news.