I have read many explanations from experts and also regular Joes regarding these two terms, and I have considered them all, as to what makes them different, or even synonymous. After taking in all of the information, and digesting it, I think I have finally realized the real and
definitive difference between these two words, and how they relate to the process of making a pot, or cup of tea. And the answer to this tea time conundrum appears to be more simple than one may think.
Back In The Day...
brew (v.) Old English breowan "to brew" (class II strong verb, past tense breaw, past participle browen), from Proto-Germanic *breuwan "to brew" (cognates: Old Norse brugga, Old Frisian briuwa, Middle Dutch brouwen, Old High German briuwan, German brauen "to brew"), from PIE root *bhreuə- "to bubble, boil, effervesce" (cognates: Sanskrit bhurnih"violent, passionate," Greek phrear "well, spring, cistern," Latin fervere "to boil, foam," Thracian Greek brytos "fermented liquor made from barley," Russian bruja "current," Old Irish bruth "heat;" Old English beorma "yeast;" Old High German brato "roast meat"), the original sense thus being "make a drink by boiling." Related: Brewed; brewing.
steep (v.) "to soak in a liquid," early 14c., of uncertain origin, originally in reference to barley or malt, probably cognate with Old Norse steypa "to pour out, throw" (perhaps from an unrecorded Old English cognate), from Proto-Germanic *staupijanan. Related: Steeped; steeping.