"justify" vs. "align" in the context of alignment

Solution 1:

Align is the correct term.

Think of align as a vertical invisible line running down the page. You can align the text left on that invisible line, right on that invisible line or have the text centered on that invisible line.

Justification is a lateral horizontal measurement based on one of two invisible vertical lines - left and right for justified text or left only for unjustified text.

Solution 2:

Whilst the modern terminology seems to suggest align is the correct phrase, this seems to be a recent innovation.

Certainly I've always used left justified and right justified and fully justified in the typing/typesetting sense... it is only since I've been doing web-based work (noting that HTML/CSS uses align) that I've found myself using align even though I still think of justifing paragraphs.

By way of clarification, text within a paragraph is justified, whereas the paragraph is aligned with respect to the margins (etc). In the accounting sense, the numbers are vertically aligned by the decimal points, whereas the currency symbol is usually left justified

Solution 3:

The question “Is it OK to call this option justify or is only align correct?” implies that an option name is sought. Both of those words are verbs. Nouns often are more suitable for use as names than are verbs. Noun forms of the words are justification:

(typography) The alignment of text to the left margin (left justification), the right margin (right justification), or both margins (full justification)

and alignment:

proper or desirable coordination or relation of components (1) or
when two or more things are positioned in a straight line or parallel to each other (2)

It appears that the Collins and Cambridge dictionaries just referenced don't yet recognize special typographical meanings of alignment. Nevertheless, my recommendation is that you use one of the words alignment, positioning, or placement as the name of the option.