Many different types/kinds of cells comprise a single tissue. For instance, the epithelial tissue of mammalian skin can contain cells that produce hair, excrete sweat, or do neither of these things but simply serve as a barrier. These cells are all epithelial tissue. Here is another example of the diversity of cell types in a single tissue: the cells of the brain are part of 'nervous tissue', but there are thousands of different kinds of neuronal cells (the precise number is growing actually; see this website, where this image was grabbed).
Blood is technically a tissue, and yet there are many, many different kinds of blood cells.
In reference to your second question, the cells share a common origin in a tissue because they come from a small number of precursor cells, like the depiction in the image above for blood cells.