What is the difference between "accumulative" and "cumulative"?

I'm having a hard time understanding the real distinction between accumulative and cumulative.

accumulative

adjective

1. tending to accumulate or arising from accumulation; cumulative.
2. tending to accumulate wealth; acquisitive.

cumulative

adjective

1. increasing or growing by accumulation or successive additions: the cumulative effect of one rejection after another.
2. formed by or resulting from accumulation or the addition of successive parts or elements.
3. of or pertaining to interest or dividends that, if not paid when due, become a prior claim for payment in the future: cumulative preferred stocks.

These definitions (and those from other dictionaries as well) say different things but I can't understand how they aren't really meaning the same thing.

Yet, when thinking about it, it seems there are some cases where it is distinctly more correct to use one or the other.

What's the difference, practically?

The big difference is that cumulative is far more common than accumulative.

At the level of actual meaning, to the extent that accumulative is used at all, it tends to refer to someone/something doing the accumulating. By contrast, cumulative is more associated with that which is accumulated.

If the sense intended is acquisitive, just use that word. In all other cases, use cumulative.

Accumulative lays more emphasis on the process of accumulating, and cumulative on the result. [Parallel to FumbleFingers' agent vs. substance distinction but perhaps an iota more transparent.]

Note that accumulative derives from ad- ("in addition") plus cumulare, "heap up", from cumulus, "heap". As noted in wiki.answers, prefix ac "replaces ad as a prefix when used in words where ad doesn't conjoin well with the root word e.g. acclaim, account, accomplice." (Ac- and ad- also are briefly mentioned in a useful chart of Roots, Prefixes, Suffixes pdf file.) The 16th-century reasons for adding on adding on to adding on may be undiscoverable; of course the two words express minutely different meanings, but whether they express a difference worth expressing is far less clear.

In modern usage, there are numerous phrases (cumulative distribution in particular) where use of accumulative would appear illiterate; typically, one can avoid accumulative altogether. Of course other forms of the word cannot be avoided, as in accumulate wealth and accumulator register.

(Editing Note: I removed an either ... or construction from the previous paragraph, in response to FumbleFingers' comment, based on my misunderstanding of "In all other cases, use cumulative".)