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What is the word that describes a word that has changed in spelling but not meaning, such as how the word "to-day" was once spelt "today"?

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The single word for this is variant. More completely variant spelling.

variant spelling

noun

A different spelling for a single word. Typically a US vs. UK or US vs. Commonwealth distinction.

For example, color and colour are the same word spelt in the American and British styles respectively. You'd think there'd be a word for this that fits into this system:

homograph

Use the noun homograph to talk about two words that are spelled the same but have different meanings and are pronounced differently — like "sow," meaning female pig, and "sow," to plant seeds. Continue reading...

homonym

A homonym is a word that is said or spelled the same way as another word but has a different meaning. "Write” and “right” is a good example of a pair of homonyms. Continue reading...

homophone

A homophone is a word that sounds the same as another word but has a different meaning and/or spelling. “Flower” and “flour” are homophones because they are pronounced the same but you certainly can’t bake a cake using daffodils.

vocabulary.com: homonym-homophone-homograph

The hetero prefix is the counterpoint to homo prefix used here. Hetero means different where homo means the same. So one might imagine hetrograph is the word you want. However:

Heterographs are words that sound the same as other words, but they have different spellings and different meanings. For the English language learner or for young students, these words can be very confusing.

google: heterograph definition

So heterograph doesn't work if you want this exact meaning. There is a very similar question on linguistics that illustrates the distinctions with a Venn diagram.

enter image description here

This originally comes from the wikipedia article on Homonym's which has a very easy to read table:

enter image description here

that is clearly missing your meaning:

      Term       | Meaning | Spelling  | Pronunciation
-----------------+---------+-----------+--------------
Variant spelling | Same    | Different | Same

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