They are many types of witch and I will name and attempt to describe a few.
1/ Hereditary = Someone who comes from a line of witches and can trace their ancestry back a fair few generations. Although it can be argued that it only takes two generations to make a line.
2/ Traditional = A witch NOT a wiccan.
3/ Kitchen = A witch whose spells are derived from herbs, cooking, baking and making the ingredients for a spell up from the items she makes herself rather than bought from a shop.
4/ Green = A witch who works with the earth and her elements, normally involving outside rituals, crystals etc
5/ Hearth = Similar to a kitchen witch but seem to be more older / motherly in outlook.
6/ Hedge = A Hedgewitch lived on the edges of the community, often on the other side of the town’s boundary hedge. They scratched out a living through herbalism, understanding nature, prophecy and divination as well as magic and healing.
There are many more, let alone other examples from around the world, but in the UK the ones above are more widely practiced.
A witch may work solitary, in a coven, specifically as e.g. one of the above or more commonly eclectically – combing elements from each of the examples.
Personally I am a traditional witch who works eclectically within a coven, although I will practice and study outside of the coven. I could claim to be a hereditary witch , but I find the term pompous. There is nothing worse then hearing witches try and out do each other with who can trace their lineage back the furthest. To me it means nothing, you are only as good a witch as the one staring back at you from the mirror.