and 
The three are entirely different. Cilantro (or coriander in the UK) has a very distinctive taste which has lemon/lime citrus notes. Some people (genetically) hate it. To them it tastes soapy. The stems give rather more flavour than the leaves. Parsley has a milder fresh flavour but can also taste slightly peppery. Celery (more especially the leaves) has an entirely different in taste and whilst having a fresh green tang contains distinctive aniseed notes.
you eat the leaves?
Yes, of course! Try them chopped on a salad or in a soup. They are quite pungent compared with the stalks.you eat the leaves?
my celery rarely if ever comes with leaves, do you grow your own?
I would eat the leaves of celery or use them in a dish. Of the three mentioned, parsley is what I mostly have on hand and hope to have some planted in my garden when it's been revived.
Oh gosh no! I'm talking about the sometimes rather pale yellowy green small leaves that are sometimes left on the top of the stalks. Sadly, as you say, these are often trimmed off. To my mind, they are the best bit. I haven't bought celery for a while but tomorrow I will now check our Aldi and Tesco to see if their celery has leaves!
I just went to look up celery leaves. Whilst you can use the leaves which might be attached to celery stalks, it seems that there is a variant called leaf celery. This is more leaf than stalk and is grown, as a herb, for the leaf. I hadn't ever heard of this! But apparently its easy to grow. I'm now wondering if this is what @Bakemehappy is referring to.
