Egotistic describes a person, a speech, or a manner that keeps coming back to how great and important the speaker thinks they are. Same idea as egotist, but as an adjective: an egotistic remark, an egotistic star. It is negative. Though actually, in real speech egotistical is far more common. Egotistic sounds a bit stiffer, more like a page than a conversation. Many people treat egotistic, egotistical, and even egoistic as one word. If you need one adjective to remember and use, remember egotistical. Keep egotistic for reading: you will see it, you just may not hear it.