Do I consider myself a psychic? No. Do I consider myself intuitive? Yes. What's the difference?
To me, it's all about what labels people are comfortable with. Me, I'm not comfortable with the word "psychic" in general. Any time anyone calls me one, it gives me pause. I feel that label is taken to the extreme in both a positive and a negative way. In the positive way, if you're labeled "psychic" you either do it full-time as your profession and you're always "ON". In a negative way, "psychic" to some people equates directly to "charlatan", which is extremely unfortunate, and a generalization of a group of people. There are phonies in every line of work; in every walk of life. Those that think psychics are a crock based on experiences with the crooked minority are closing themselves off to the psychics that are there in the service of growth of the human spirit.
So based on the connotations of the word "psychic", I choose to identify myself with the word "intuitive" instead, something I believe everyone is, some more than others, and something that can be cultivated and developed with practice. Not all tarot readers read intuitively. There are some that memorize the standard meanings of all 78 cards and their reversals, and then read based on that. When I began reading, I memorized. Memorization is a great thing for a beginner. As they say, you need to learn the rules before you break them. As I read the cards more, I began to trust in what I was seeing in the pictures more than what I had memorized for a card. From then, I associated the memories from my own life that the cards evoked to what my client was asking about when I read for them.
My sister once introduced me to a friend of hers as psychic. It was possibly the ONLY time I've ever felt comfortable with the designation. So call me a psychic if you want to, but I might look at you askance.