Smart casual is a less formal extension to business casual. While business casual is great for the office and meetings, smart casual is for everything outside of work. Unless you work in a very informal environment. Then smart casual might be your go to for the office.
You can wear a plain, toned-down t-shirt under a jacket for smart casual look, any t-shirt that has a print of some sort is more of a casual look, not smart casual. If you wear a t-shirt without a jacket, it is more of a casual look.
If you opt for a shirt, you can add colour, or choose checked. Compliment it with a blazer or a pull over.
As for trousers, like with shirts you can wear more colour than in business casual. Jeans, smart chinos. Ripped jeans and shorts are a casual look, not smart casual.