There are several differences in the Ukrainian alphabets used in the diaspora and in Ukraine, in particular, what we call the alphabet, the way we pronounce the letters, the melody we use when singing the alphabet (or the lack thereof a song), as well as the difference I only recently discovered — the placement of the soft sign.
In Ukraine the soft sign “ь” doesn’t come at the end of the alphabet as I learned, but third to last. It was quite a big shock for me to discover. However, this was a relatively recent change. In 1990, the soft sign was moved from the end of the alphabet to the place after the letter “щ” as it is in the Russian alphabet. I’m surprised it wasn’t moved back a year later when Ukraine gained its independence.
First of all, we usually say “азбука” or “абетка” while in Ukraine it is more common to say “aлфавіт” or “абетка” (for children).
When we (at least my Chicago diaspora community) sing/say the alphabet, we just say the sounds (a, b, v, h, g, d…), while in Ukraine they add an “e” to most of the consonants (a, be, ve, he, ge, de…) as seen below:
I learned the alphabet to the melody of the song “Ой там на горі січ йде,” a song of the Sich Riflemen, which is another sign of the Galician influence on the community. But I’m not sure how widely this was/is used in the diaspora outside of my specific community.
And in terms of the placement of the soft sign (which by the way we call “мягкий знак” not “м’який знак” like in Ukraine), not only does it always come at the end of the alphabet, we even would sing the words “мягкий знак, на, на кінці” at the end of the song.
To illustrate the difference, below are the two alphabets. The first image is the alphabet that hung in my room when I was a child. The second is a contemporary alphabet used by children in Ukraine today. Note the last row and the placement of “ь.”