I think the term “feeling called” a lot of times can be used interchangably with discernment. By the way, “discernment” is a very Catholic word, which you almost never hear in Prot. circles, but “being called” is quite common, so depending on whether the person is Catholic or Protestant, they could be talking about the same things.
To me, “being called” means that you have recognized the big things God is asking you to do, like being called to the priesthood. Or being called to marriage.
Sometimes “the call” is just that. Not that the phone rings or anything. But that Jesus specifically asks you to do a specific thing. Look at Bl. Mother Thresa of Calcutta. She was called, quite literally, to start the Missionaries of Charity. Jesus literally asked her to do it.
I was literally called to become a Catholic. God told me to “go be Catholic.” Just like that. Many times - because I didn’t want to listen the first time. I can’t explain why God did it the way he did, but he did. That happens to me sometimes. Frankly, I’d rather it didn’t, but there you have it.
When “being called” isn’t so literal, then I think it’s that sense that you know deep within yourself what it is that God wants you to do. And yes, there is a spiritual component to it, because how are you going to know what you are called to do unless you have first, asked God to reveal it to you, and second, were quiet and still long enough to hear his answer. And no, when God does call, he may not (probably won’t) ask you to do something that you feel comfortable doing or are even sure you will enjoy doing. But when you say “yes”, I guarantee you there will be no regrets and you will always be thankful that he called and you answered.
Kris