More specifically, what effects does withdrawing an application have? And what effects does expressly abandoning an application have?
The text of the MPEP sections is pretty clear. They really are nothing alike. A key difference is it withdrawal is withdrawal from issue. MPEP 1308. It is only relevant after a Notice of Allowance. In fact after a NOA you can’t even expressly abandon it without an accompanying withdrawal from issue. Also, the office can cause a withdrawal from issue but only you can expressly abandon.
Withdrawal from issue just puts it back into examination where it might be fixed and then proceed to issue later. There are many reasons for withdrawal from issue, like one claim is not patentable, that are fixable.
The effect of express abandonment MPEP 711 is that the application is dead. If it has not yet published that might stop publication if it is received early enough. MPEP 1125. Any later than four weeks before publication and it publishes. It might still publish even with more than four weeks.
By the time an NOA is issued the application is likely published unless it was an extremely fast prosecution or a non-publication request was filed. If the issue fee is not paid and you want to avoid the issuing and public exposure of an application under a non publication request all that is needed is to not pay the issue fee. It will not issue and not become public if it was already public. After paying the issue fee you can withdraw only for certain reasons. See MPEP.
Note - abandonment of an application is not the same as abandonment of an invention. Do not declare you have abandoned an invention lightly.