Mixed-integer (Linear) Programming (MILP) standard/canonical form

Question

Is there a standard or canonical form for mixed-integer (linear) programming problems? For linear programms the standard form is sometimes given by: $$ \max_{\boldsymbol x} \boldsymbol c^T \boldsymbol x\\ \text{s.t.} \boldsymbol{Ax} = \boldsymbol b\\ \boldsymbol x \geq \boldsymbol 0 $$ or$$ \max_{\boldsymbol x} \boldsymbol c^T \boldsymbol x\\ \text{s.t.} \boldsymbol{Ax} \leq \boldsymbol b\\ \boldsymbol x \geq \boldsymbol 0 $$ Mostly, the MILP problems are just explained by "require some variables to be integer" (e.g. Wikipedia). So I was wondering: Is there a standard form for MILPs or the more general MIPs?