After asking what the difference is between a gerund and a participle, I began to wonder if all gerunds end with -ing, since I couldn't think of any that didn't. If they do, why?
To answer the original question:
Yes, gerunds all end with -ing, simply by definition. A gerund is, in Latin, a form of the verb which can be construed as (i.e. has functional characteristics of) a noun – it can act as subject or object of a verb, for example, or can take a plural ending. In English, the only category which meets this definition are "verbal nouns" or gerunds, which consist of a verb and a special -ing suffix which turns them into nouns. Although they look like present participles, they are morphologically separate, as we will see...
To answer the bounty question:
The gerundial -ing and the present participal -ing are, in fact, two different suffixes.
Let's start with the gerundial -ing. This is related to modern German -ung and modern Dutch -ing. It started life as a suffix forming nouns of action in Old English, usually written "-ung" - "gaderung" (gathering), "ceaping" (buying and selling). These gerunds were originally abstract, but even in Old English they started to develop into nouns of completed action, etc.: "bletsung" (blessing), "weddung" (betrothal). They subsequently developed plurals, and sometimes became concrete: "offrung" (offering). These uses all developed in the Middle English period, and by late Middle English they were well-established, particularly the gerundial use. Essentially, therefore, there never was a competing form for the gerundial -ing. It started off as "-ung" or "-ing" and continued in that form.
The present participial -ing, on the other hand, started off life as the -ende / -ande form that you refer to. It's related to modern German -end, and Swedish -ande. Even in the Old English period, -ende was often weakened to -inde, and by early Middle English there seems to have been a tendency to confuse "-inde" and "-inge" (this is particularly noticable in Anglo-Norman manuscripts of the 1300s.) Northern forms of the language retained -inde forms, however, though the distinction is not particularly obvious in Northern dialects, since both "g-dropping" and the tendency for "d" to be diminished after a preceding nasal consonant in an unstressed syllable (see, for example, the tendency to say "an" or "en" instead of "and" - "rock 'n' roll") means that either -ing or -ind may generally be produced as -in'.
It's possible that, in the later Middle English period, the development and prominence of the gerundial -ing, perceived as a quasi-verbal ending, also helped to strengthen the participial -ing. But their origins are quite separate, with participial -ing as a diminished form of -ande, while gerundial -ing has undergone few changes from its original form.
Information from my own knowledge, and from the OED's entries -ing, suffix1 and -ing, suffix2. Examples taken from OED, because they are excellent illustrations of the points.
Yes all gerunds end with -ing. Asking why is a bit of a tricky question, but basically it boils down to the fact that there were no historical processes that messed this up.
The English past tense and past participle, for example, are very complicated for reasons going back to PIE. Germanic languages all use something called ablaut for past tenses and past participles, which is a kind of vowel change, and this accounts for English tense sets like sing/sang/sung. However, even in Proto-Germanic the ablaut process was complemented by a set of endings for "weak verbs" that used a dental morpheme to indicate past tense. This is the ancestor of the current English past tense marker -ed. However, even the weak verbs have been irregularized by various phonological processes, giving us "irregular weak verbs" like teach/taught.
The English gerund ending never participated in ablaut, though, which eliminates one major source of complexity. Furthermore, the phonological changes that created the irregular weak verbs did not affect the suffix -ing. Finally, the very fact that there are no verbs with irregular -ing forms acts as a strong disincentive to ever create any, as any phonological change that would make the gerund irregular is quickly corrected by analogy.
It seems to me there is sometimes a mere semantic sliver between forms ending in -ing (which we call gerunds) and those ending in -ion (which we call nouns).
For instance, clocks used to have to be corrected for the "equation" of time. (Because before the era of the telegraph or the railway, sundial time was the reference standard, and clocks did not automatically show noon as the sun passed the meridian) Now it's the other way around: clock time has become the reference standard, and in modern times we would say it is sundials which are corrected for the EQUATING of time, which is a gerund. But it has the same significance that "equation" used to have.
At any given time, the choice of the -ion form vs the -ing seems to me to be guided largely by fashion (eg dispersal/dispersion), but I'm no grammatician.