Accounting profit in macroeconomics as compared to microeconomics In Macroeconomics (2019) on p.103, it is argued that the reason there exists profit in an economy is that most firms own rather than rent capital. Thus:

But, Microeconomics assumes a different definition of economic profit. It is the surplus after deducing opportunity cost and implicit costs.
Why is there a difference in the definition of accounting profit between the fields of Macroeconomics and Microeconomics?
There is no difference in definitions. In macroeconomics the economic profit is also surplus after accounting opportunity cost and all  other implicit and explicit cost.
What the equation above says is just that the accounting profit also contains return to capital. That also hold in microeconomics for any firm that owns and uses capital in its production function.
For example, typical microeconomic profit equation will be given as:
$$\Pi = PF(K, L) − wL − rK$$
where $P$ is price, $F(\cdot)$ output, $w$ wage, $r$ return, $L$ labor and $K$ capital. In the equation above the firm rents capital from some other firm. However, if If firm owns its capital rather than rent it the $rK$ will belong to the firm owner and be part of their profit (you can think of it as firm 'renting' capital from itself).
The equation above simply states that the accounting profit will be sum of economic profit (i.e. surplus after all costs are accounted for) plus any return on the capital they provide.
In fact in both microeconomics and macroeconomics this extends even further. If firm owner provides also labor/entrepreneurial labor, then the accounting profit will be actually given by $\text{accounting profit}  = \text{Economic Profit} + wL + rK$.
Again this is not something that would be different in economics. To see this just rearrange the expression for economic profit.
$ \text{Economic Profit}  = \text{accounting profit} - wL - rK$
The above literary tells you that economic profit is surplus after accounting the explicit and implicit costs of labor and capital. The wage and rent should already reflect the opportunity costs of using that labor and wage elsewhere.