Why yes, that word does mean what I think it does.
If we're talking about what inflation is, well, prices going up is not inflation to begin with. The expansion of the money supply is inflation. Prices going up is merely a potential symptom of inflation.
Inflation does in fact harm the poor dramatically more so than anybody else. They're the most susceptible to rising prices, their incomes rise the slowest, and they have no capital or assets to leverage to keep pace with inflation through hedges (such as stocks, gold, commodities in general, housing, etc).
Incomes do not inherently go up hand in hand with prices. In fact it's the exact opposite, the greater the inflation the less able incomes are to keep pace. America is dramatic proof of that over the last 40 years, as the cost of major goods such as housing, education and healthcare have vastly outstripped gains in income.
Your theory that wages inherently keep up with inflation assumes that there are no spin-off consequences to inflation, that's blatantly not correct. It generates a downward spiral, cascade effect; just ask Argentina how that works, their economy has been getting hammered by it the last few years. As you expand the money supply, devalue your currency and generate inflation, all sorts of costs from external sources begin to climb, such as the cost of imports (raw goods like plastic or steel, completed goods like toasters, commodities etc). This one effect alone guarantees domestic wages can never keep pace with inflation.
Inflation also destroys savings, and the poor always have the smallest base of savings to begin with, and are least able to shift their savings into higher yielding investments.
There are numerous recent examples from around the world where inflation outstrips wage gains.
Brazil is an obvious recent example of it, the cost of goods in Brazil is outrageous, and was one of the reasons for their recent riots. The high inflation there, requiring incredible interest rates to fight, has far outstripped their wage gains. Venezuela and Argentina are two other recent examples of it. And there are extreme examples of it, in which the people of a country have been wiped out by inflated prices while their incomes did not keep up (Zimbabwe is an easy example of that).