Learn English – Does “recenter” have a British spelling

More accurately (and I had to look this up) the OP is actually asking about "heterographs": words that sound alike but have different spellings and meanings. Homophones may be either heterographs or heteronyms (words that have the same spelling and different meanings, and may or may not have the same pronunciation, e. g. desert/desert). Examples that native speakers frequently get wrong are principle and principal, affect and effect, discrete and discreet, and even too and to and its and it's. For a long list of these, see http://www.spellingsociety.org/journals/j4/heterografs2.php . (Personally, I don't think that a dictionary will help much in identifying these; there are too many words that are not such to make the search easy.)

If I understand the logic behind your question, you are asking:

Since movies is plural, why is the singular movie and not movy?

In general:

Well, just because there is a common and helpful rule that states

A noun ending in a consonant and then y makes the plural by dropping the y and adding -ies

this does not mean that you can always apply this rule backwards to any plural word ending in -ies to get the singular of that word.

That is, there is no rule that says a word whose plural form ends in -ies comes from a singular form that ends in consonant plus -y.

You can apply the rule backwards, when it was originally to a word, as in

daisies : daisy
ponies : pony

But you cannot apply the rule backwards when it was not originally applied. Thus the following does not work

monies : mony

(Note that money has two plural forms, moneys and monies.)

In Particular

And the following does not work:

movies : movy

Because the singular of movies is not movy but movie. The why of that has to do with movie coming from moving picture. Mov(ing picture).

The -ing picture was replaced by the ending -ie. I suppose it could have been replaced by y (after all, we have such nouns as gravy.

I suspect that movie(s) originally had a diminutive meaning, in which case the ending -y seems to be fine only in words whose last consonant is doubled (doggy, granny) while -ie goes with those kind of words (doggie, grannie) or...

with words whose consonants are not doubled (sweetie, birdie). I guess movvy didn't quite work, any more than movy.

A similar word to movie, now outdated, is

talkie

It has the plural talkies. The word talkie apparently does not come directly from talking pictures, but from movies. The mov- was replaced by talk-.

Note that we have 'walkie-talkie'. This conforms with -ie usage in words whose ending consonant does not double. But later on came the form 'walky-talky'. One can only guess why this variant spelling came about.