a replicative plasmid is a plasmid which, once inside its bacterial host cell, will remain in its extra-chromosomal form; its replication is autonomous and does not depend on the replication of the chromosome.

On the other hand, an integrative plasmid is a plasmid which cannot be found in an extrachromosomal form, it must integrate the bacterial chromosome, it cannot replicate autonomously, its replication depends on the replication of the chromosome.

Since Sofiane Benyamina already answered part of your question, I'll take a stab at the other part:

Addgene says the backbone is of pMSP12::mCherry is pFPV27 which has a Mycobacterial origin of replication, so it's probably a replicative plasmid.

My educated guess as to how this vector was made is starting with pFPV27 which has a mycobacterial origin of replication and a green fluorescent protein gene (GFP) without a promoter -> cloning of "mycobacterial strong promoter 12" (Hence the MSP12 in the plasmid name) in front of GFP to make pMSP12::GFP -> Replacement of the GFP in pMSP12::GFP for mCherry to make pMSP12::mCherry.

pFPV27 citation: Article The identification of Mycobacterium marinum genes differenti...

Addgene plasmid URL:

https://www.addgene.org/30169/

Classical genome modification procedures are based on the use of integrative plasmids harboring homologous regions that will undergo simple or double crossover.