There is a difference between the pronunciation of א and ע. The letter א is "silent", as are the English vowels. But the letter ע is not, it has a throaty sound.
In today language it sounds usually the same, but the difference exists (even if not used)
Watch this great video: https://www.youtube.com/watch?v=2-9MMghUsLo
If you want them to be different, then you may say עני the way it is supposed it be, i.e. with the guttural sound. It is quite distinctive.
Most Israelis do not speak like that anymore but some still do. For instance, the Yemenite Jews who never stopped speaking Hebrew since the first temple. And Arabs speaking Hebrew.