Personally I almost never use MCB in 24VDC applications because a device like a SEL1400 is more cost effective and offer some nice features. I only resort to MCBs if the inrush of the device is higher than the maximum selectable current in the electronic protection module (may AUMA be forever damned with their ridicolously oversized motors).

As far as VFD are concerned I use regular MCB instead of the suggested MCCB or MPCB because they don't make any sense, an inverter is not an inductive load and it has it's own motor protection functions.

Lastly, most modern starters have an integrated current monitoring system, because of this reason I don't use regular MPCB but the ones without thermal protection, they are cheaper and I keep the proper selectivity. Besides, a starter can be remotely reset, a tripped MPCB requires someone to go to the plant and turn the lever.

AC MCB has labels of the terminals as LOAD and LINE terminals whereas the DC MCB will have positive (+) or negative (-) sign on its terminal. 

If the properties of the AC MCB and DC MCB are looked for the differences among them than the only noticeable difference is the breaking of AC MCB and DC MCB. It is harder to break a DC MCB as compared to an AC MCB. AC MCB is extinguished with the help of zero crossings but a DC MCB is extinguished with the help of a mechanical interruption or with cooling. DC MCBs open faster as compared to AC MCBs.

For more details, you can check out this article: https://electgo.com/resources/mcb-for-ac