I have called myself a "continuationist", but that's with a lot of asterisks and footnotes attached.
I don't believe in Charismaticism as understood within those modern movements. Which means I am, at best, suspicious of many claims made; and concerning the more extreme claims not merely suspicious but outright in opposition as being outside the pale of what can be called acceptable in the Christian Church.
As
@Daniel9v9 said, this continualist/cessationist friction is really unique to a certain spectrum of Protestantism, and isn't particularly applicable to those outside of the Reformed and Reformed-inherited traditions. So when I call myself a "continuationist" I'm using a term that is probably not completely correct in the context the term is usually used. Rather what I am saying is that I do not hold to a dogmatic position that, at some point, whether suddenly or gradually, certain charisms of the Spirit completely ceased.
I am entirely okay with the idea that someone might receive the gift of (e.g.) tongues. The asterisk and footnote to that is that I don't consider what is often called "tongues" in the last ~150 years to be that charism as spoken about in Scripture and which was historically something that has happened in the Church. But if someone, never having been taught or exposed to, say, French or German suddenly is speaking fully coherent phrases in French or German, and it is understood either by translation or by a native speaker of that language, and it is edifying and in harmony with Scripture and true Christian doctrine--then what should I do other than offer God praise for His gifts?
However, my personal experience, both inside and outside of Pentecostal and Charismatic traditions; and someone who "spoke in tongues" for nearly 15 years as a regular part of my personal devotional life--I'm simply not convinced that what I saw--and what I did myself--is truly and validly a biblical and Holy Spirit-originated phenomenon. That is going to be very offensive to some people. That isn't my intention, but that is where I am at as far as this conversation goes.
So that means I would say this, when I call myself a "continuationist" it means: Charisms? Yes. Charismaticism? No.
-CryptoLutheran