At my old job, I knew someone by the name of Takahashi (last name).
Sometimes I'd see their name spelled 高橋 and sometimes 髙橋.
Why was 高 sometimes used and why was 髙 sometimes used?
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The short answer is that 髙, or 「はしごたか」, is an alternate form of 高, and as such some people might use it. It does not represent a new/old character relationship (新字体・旧字体), however 髙 could have been a hand-written form.
Apparently, though, this character is a little special, and it seems as though you're not technically allowed to use it in names. This article put out on the website of 三省堂, a prominent Japanese dictionary publishing company, comments on the character's history. It seems that 髙 was originally proposed as a form to consolidate and make consistent the characters used in printing type (活字字体). There was, however, a concurrent movement to reduce the stroke order and complexity of characters in the 当用漢字, the precursor to 常用漢字, and the change was scrapped. There were various revisions and updates to the naming standards, but the new printed version "髙" was continually left out (despite continued attempts to use it).
Other places say that the 髙 form existed as a hand-written form, and that now that 高 is standardized, 髙 is relegated to the status of "俗字."
So with your previous colleague, my guess is that they wanted to use 髙, or maybe that it was in the past or something. It's hard to type now as well, which would make it even more likely for someone to use 高 instead.
If my understanding is correct, then this person's name is officially registered with 高 instead. The alternate form does not appear on the 人名用漢字表 either in the standard kanji or in the approved alternate forms.