The difference in these two sentences would be "THE school uniform" - the, we know which school uniform we are both talking about; "A uniform" - a, one of many uniforms, we don't know which one.
These are articles: a, an, the.
Countable and uncountable refers to nouns: things we can count (chairs, books, students, cups), and thinks we can't count (milk, coffee, wine, water).