Determiners are words like "the", "a", and "my" that come before nouns and provide information about the noun but don't have specific meanings on their own. Adjectives are words like "blue" and "tall" that describe or modify nouns and can have comparative and superlative forms with "-er" and "-est". Determiners are function words that precede nouns while adjectives follow nouns and provide descriptions, and personal and possessive pronouns cannot be used as determiners.