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).

As a noun, it is always countable. In those sentences, you see the articles 'the' and 'a'. Those are both equivalent to 'one', although 'the' can sometimes refer to a group or whole. It's confusing because some things, clothing especially, are understood based on logic. For example: "Students wear uniforms to school." "Students wear a uniform to school." These sentences have the same meaning because we know that it means each student will wear their uniform to school. English isn't always clear. Sorry for that.

In the first sentence, "the school uniform" refers to a certain style of dressing. For example, white shirt, grey trousers, green coat (with the school insignia). The second sentence means one set of these particular clothes. I don't think it's a question of countable/uncountable. In the case of "military uniforms", this could mean various styles of dress (according to rank and division), or many sets of one type of uniform.