Acting:- you are put to a promotion board and promoted, this is relayed to your brigade and if your brigade ok's it then it is put in part 1 (or 2, not sure which) orders. You then remain acting until either a period of probation has passed or you have passed the command course required to hold the rank substantively.
My understanding is that Substantive rank is much harder to take away hence the reason you get acting rank to make sure you are not a biff before you are made substantive.
Local Rank, is granted at Regiment level and does not have to be approved by Bde, it is usually granted to attend courses that are rank barred such as PTI (L/Cpl)
Both acting and local rank may be paid or not paid which is dealt with under the regs for higher duties pay.
I think during WW2 there many cases of officers being at a local rank two or three above their Substantive rank. So you had sub Major, acting Lt Col & Local Col or even Brig. It all came crashing down in peacetime.