Uniform convergence: $\sup_x|f_n(x)-f(x)| \to 0$; pointwise: for each fixed $x$, $f_n(x) \to f(x)$

Pointwise convergence: $\sup_x|f_n(x)-f(x)| \to 0$; uniform: for each $x$, $f_n(x) \to f(x)$

Both are equivalent when $f$ is continuous

Uniform convergence is weaker than pointwise convergence