Yes, simply, they are “two separate processes”, but sanctification encapsulates mortification in the overall atoning work of Christ. By that, I mean that mortification is a byproduct of the Spirit’s sanctifying work, and this is a distinction in itself.
I would like to answer ‘yes’ to your second question, but I think there may need to be some clarification. If one ‘pursues’ sanctification, mortification will not necessarily sprout forth. Why? Because I believe no one ought to ‘seek’ processes – they ought to seek Christ. The unification of sanctification and mortification only comes from Christ’s overall procession of salvation. Sanctification only encapsulates mortification because they are both under the same soteriological source. Thus, if one ‘seeks’ sanctification, they may be missing the source, and, consequently, other soteriological process may be thwarted.
Processional Christianity is a form of religiosity. Christ motions the processes from His person. You see? It may be a picky way to answer your question, but I think it is a very insightful distinction. It is true, that I do not necessarily seek holiness; I seek Christ, and in that utter pursuit, holiness – sanctification and mortification – uncontrollably comes forth. My ‘virtue of pursuing’ is rendered useless unless Christ is behind/in me pushing me forward by His grace.
Is that understandable?