They all sound the same...

Q: I am in love with your blog. It is so informative. (thank you, dear reader).
    Is Twinkle, Twinkle Little Star and the Alphabet song (a,b,c,d,e,f,g.....now I know my a,b,c's....) the same rhyme? Which one came first?

A.You have a great ear.

According to Wikipedia, 'Twinkle, Twinkle Little Star' combines the tune of the 1761 French melody, 'Ah! vous dirai-je, Maman" with an English poem, 'The Star', by Jane Taylor,  published in 1806.

Many songs in various languages are based on this French melody, including the Alphabet Song you mention (1834), and Baa, Baa, Black Sheep.

Wikipedia dispells the misconception that Mozart wrote this music, although it says he did write 12 variations of it. And the original French song was not a nursery rhyme intended for the ears of children. The main thrust of several versions of the song is a girl confiding a tale of love or seduction to her mother.

Five complete verses of Twinkle, Twinkle Little Star are taken from the Oxford Dictionary of Nursery Rhymes:

Twinkle, twinkle, little star,
How I wonder what you are!
Up above the world so high,
Like a diamond in the sky.
Twinkle, twinkle, little star,
How I wonder what you are!

When the blazing sun is gone,
When he nothing shines upon,
Then you show your little light,
Twinkle, twinkle, all the night.
Twinkle, twinkle, little star,
How I wonder what you are!

Then the traveller in the dark,
Thanks you for your tiny spark,
He could not see which way to go,
If you did not twinkle so.
Twinkle, twinkle, little star,
How I wonder what you are!

In the dark blue sky you keep,
And often through my curtains peep,
For you never shut your eye,
Till the sun is in the sky.
Twinkle, twinkle, little star,
How I wonder what you are!

As your bright and tiny spark,
Lights the traveller in the dark,—
Though I know not what you are,
Twinkle, twinkle, little star.
Twinkle, twinkle, little star,
How I wonder what you are!