What's the difference between an Alif and a Hamza? We all know that Alif is written like ا and Hamza is written like أ But apart from that what is the difference between them?

Hamza is a consonant like all other letters in the Arabic alphabet. That means it has a sound (the glottal stop) and can be used just like other letters.

Fun Fact: Hamza is derived from the verb hamaza (هَمَزَ‎) meaning 'to prick, goad, drive'.

Alif on the other hand is a vowel, just like Fatha, Dhammah, and Kasrah. And it does NOT have a sound. It can modify the sound of a consonant but doesn't have a sound of its own.

That means two things: 1. Alif cannot occur on it's own. Just like Fatha, Dammah, and Kasrah can't.

2. Alif cannot come at the beginning of a word. Since it must always have a consonant preceding it, whose sound it will modify.

Fun fact: Together with Hebrew aleph, Greek alpha and Latin A, Alif is descended from Phoenician ʾāleph

If you said it is a Hamza, you are correct, since Alif cannot occur at the beginning of a word. So why there is no sign on top of this Alif to mark it as Hamza?

In ancient Arabic ا was used to express both a glottal stop (consonant) and also a long vowel. However as the usage of the long vowel increased in Arabic language, it led to orthographical confusion.

To avoid this confusion Arabs started writing a small ء on top of the Hamza which was being used as a glottal stop (consonant) and called it Hamzat-al-qaṭ‘  هَمْزَة الْقَطْع (the Hamza which breaks, ceases or halts), since the sound of Hamza closes the vocal cords (glottal stop).

Fun fact: This sign ء is actually a chopped off ع from the ع of هَمْزَة الْقَطْع

Since Alif cannot appear at the beginning of the words so there was no possibility of a Hamza occurring at the beginning of the word being mistaken for an Alif. Hence they never bothered marking the Hamza at the beginning of the word with a sign.

However, this Hamza which occurs at the beginning of a word was called the hamzat al-waṣl هَمْزَة الوَصْل (the Hamza which attaches, connects or joins) since it is only pronounced if at the beginning of an utterance, otherwise it is assimilated.

Although in Quranic orthography (spelling) Hamzat-al-waṣl is given a special sign, a chopped off ص, like so ٱ‎

Fun Fact: In the IndoPak masahif Hamzat-al-wasl doesn't have the waslah sign and is written like a regular Alif.

Hamza has a lot of complicated orthographic (spelling) rules. But that is a story for another day!