What is difference between limerick and sonnet?

A limerick is a five line poem, usually with a humorous subject, usually in a trochaic metre, rimed

AABBA

(the B lines are nearly always shortened, and regularly halflines):

There was a young lady from Deal

Who was totally lacking appeal;

"Though I try and I try.

I just can't hook a boy!

I'll just have to marry a seal!"

A Sonnet is nearly always serious, has fourteen lines, and is usually (in English) in iambic pentameter.

I touch the curtain. What's left of the day

Draws longitudes across your bedroom wall.

The room is a cartographer's display

Of vectors and projections, where we're small

And plottable. I wonder if someone

Here before me would notice the same thing

And think about its transience. The sun

Almost behind the hospital now, sinking

Down in the orange litter of its cranes

That almost spell-out letters ... But I'm stuck

If I can read them. All the weather-vanes

Show different ways. The unexpected dark

Wraps its magnetic baffle round the earth.

You draw my flesh. See. You are my True North.