What are the differences between mashing and steeping grains in preparation

The end result is the same, but mashing implies that enzymes are converting starches into sugars. These enzymes work when held around 150°F. The two enzymes are alpha and beta amylase. Alpha works more at higher temperatures (optimal at 158°F) and cuts starches randomly into long chain sugars (only some of which are fermentable). Beta works at lower temperatures (optimal at 145°F) and cuts starches at the ends to create 2-glucose sugars (maltose) (which are fermentable). A balance is usually desired and usually ranges from 148-152°F, but higher and lower mash temperatures are certainly possible.

Steeping does not require mashing. Grain like crystal malts or roast barley have been fully mashed in the husk. This occurs during the roasting process. Hot water is required only to dissolve the sugars inside.

(Yes, it's semantics: the words have different meanings. :)

Mashing is the enzymatic conversion of starch to sugar, using alpha- and beta-amylaze naturally present in grain at the specific temperatures to activate them (~150°F).

Steeping is using hot water to extract flavor and color compounds from grain.