Arabic script is used for several other languages. Farsi, Urdu, and several African languages use the Arabic script till this point in time. Turkish languages and Malay have also used it historically. Arabic is sometimes written in different hands, each is appropriate for certain settings. Hands are very similar and learning to read one takes you 90% of the way to learning all the others. Writing in different hands is another question, Arabic calligraphy is an artform. It takes a lot of practice and it both has strict rules about letter specifications and great freedom in their shapes.
Here are some of the more common hands:
Naskh
Naskh literally means "copying". It was historically used for copying
books and documents. Naskh is very clear, the letters look very distinct
and spacing is usually generous. Angles are very acute and the letters
look very square. This is the standard font, it is used in newspapers,
subtitles, most documents, and in primary schools. In other words, this
is the Arabic Times New Roman. This is the font I used in all words here.
Thuluth
Means triple or triad or something. I think this has to do something
with the ratio of letter height to width. Thuluth is very decorative, letters
have standard forms but a lot of attention is paid to the way they look
and less to the clarity of the word. Letters are usually written with obtuse
wide curves and very relaxed angles. Thuluth can be used to write any text
but usually because it takes up space it is used for titles or credits
in a movie or adds or something like that.
req3ah
Req3ah means rag. Enough said, it looks like a rag! This is the most
common written form. It actually looks quite different from naskh. The
text is kept mostly above line. Letters with circles (like qaph) are written
with solid circles. Any two dots above or below a letter are amalgamated
into a dash (-), while three dots are changed into a v or lambda shape.
This is used to write almost everything, only people with a lot of spare
time use naskh (yawn).