In its most simple form, "hard" cessationism denies any presence of the Holy Spirit and "soft" cessationism only denies the continuation of the ecstatic manifestations (gifts) of the Spirit while holding firmly to supernaturalism.
It's occurred to me that there might be two varities of non-cessationism, too:
1. Hard non-cessationism: all of the gifts of the Holy Spirit have continued in the same form ever since Pentecost.
2. Soft non-cessationism: all of the gifts of the Spirit have continued since Pentecost, but certain gifts (e.g., prophecy, healing, etc.) manifest themselves in different form than they did in the ministries of Christ and the apostles.
Of today's charismatics, I'm sure that the vast majority are soft non-cessationists. They believe in modern-day prophecy, healing, etc., but they admit that their gifts are not identical to those manifested in the ministries of Christ and his apostles. Some charismatics have claimed that God will at some point in history restore something akin to the full-powered gifts to the church, but so far such claims have not seen fruition. Only a tiny fraction of charismatics would claim that the full-blown gifts--authoritative prophecy, etc.--have continued to this day. So, although charismatics claim that the gifts of the Holy Spirit haven't ceased
, they generally admit that they have changed
since the passing of the apostles.