I always think of it as a venn diagram of ethnicity and religion.
With a Jewish mother by descent, or an orthodox conversion, you are Jewish by Orthodox (halachic) standards. Provided your mother was halachically Jewish at the time she gave birth to you. So if she converted after your birth, you would need to convert too in order to be Jewish.
Liberal and reform accept paternal descent and conversion.
Large numbers of people have some Jewish ethnicity, and they may or may not feel connected to that. Some people were not raised with any of the traditions but their Jewish ethnicity and cultural identity is still very important to them.
Being Jewish by orthodox standards becomes important at major life events if you want those to be under orthodox auspices. In Israel this is even more pronounced but that's a whole other topic.
Otherwise, I think most people are a mish-mash of practice, ethnicity, culture and identity and love their lives as such doing what feels right to them.
For non-religious events, eg social and work networking groups, being Jewish is often self defined - if you have some Jewish connection by heritage or practice, identify as part of Am Yisrael, don't make things awkward by talking about another religion, and you feel Jewish, then you are Jewish.