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Maybe the OxED better explains it. For vial it has an explicit synonym of phial:

Etymology: variant of fyole, fiol, fiall, etc., phial n. See the note on the letter V.

And, here is a lengthy note on the letter V:

the 22nd letter of the modern English and the 20th of the ancient Roman alphabet, was in the latter an adoption of the early Greek vowel-symbol V, now also represented by U and Y (q.v.), but in Latin was employed also with the value of the Greek digamma (viz. w), to which it corresponds etymologically. When not purely vocalic, it still denoted this sound at the time when the earliest Latin loan-words were adopted in the Teutonic languages; consequently such words beginning with v appear in Old English with w. Under the Empire, however, the semi-vocalic sound gradually changed to a bilabial consonant, and finally became the labio-dental voiced spirant now denoted by the letter in English and various other languages. This development did not take place in Old English; and no v, whether bilabial or labio-dental, occurred initially in the older Teutonic languages, although the sound was common in other positions (in Old English denoted by f, in early texts by b).

In Old English dictionaries there is thus no set of words with initial V, one or two Latin words adopted at a late period usually appearing with f, as fann, fers (but also vers), from Latin vannus, versus. The first appearance of V-words is found in those Middle English texts which begin to show a distinct French influence, as the Ancren Riwle; even early writers like Orm and La?amon, while not free from the use of French words, do not employ any beginning with v. The number of such words steadily increases in later texts, and is subsequently greatly reinforced by direct adoptions from Latin, by new formations on Latin stems, and by adoptions from other Romanic languages. The other sources of initial V are of minor importance. The change of w to v, which took place in the middle period of the Scandinavian languages, is represented in a few words, as Valhalla, valkyrie, viking, but otherwise the words with this initial are chiefly derived from languages not directly related to English. A small number of words, however, as vat, vixen, exemplify the voicing of f- peculiar to southern (now only south-western) dialects. This change is not indicated in Old English spelling, and how far it had developed in speech is uncertain, but in southern Middle English texts all native words (rarely those of French or Latin origin) beginning with f may appear with v- (or its equivalent u-); the more important variant forms due to this cause are entered in their places below. Conversely words properly having v- are occasionally written with f-, and there is evidence that this is not merely graphic, but represents an actual pronunciation. (‘Euen so oure Englishmen vse to speake in Essexe, for they say fineger for vineger, feale for veale, & contrary wyse a voxe for a foxe, voure for foure, etc.’ 1546 Langley, tr. Pol. Verg. de Invent. i. vi. 14.)

When not initial, v occurs freely in native words as well as in those of Latin or other origin. In the former it represents Old English f when voiced, as in ?fen even, drífan drive, lufu love. The use of f (or ff) in such words was partly retained in Middle English (and especially in Sc. down to the 16th century); but even in late Old English u is frequently substituted, and in early Middle English (as in medeval Latin and Old French) u and v come into general use to denote the sound in all positions. It was only in the 17th century that these two letters, both of which had been employed in a double function (see U), were finally distinguished as vowel and consonant; and down to the 19th century words beginning with either letter continued to form one series in dictionaries.

The best that I can get from the above is that v and f are very similar and the different usages are within Great Britain itself and there is not a British/American English thing.

I happen to note that calves being the plural of calf is likely related to the above.