Tissue (biology): In biology, tissue is a cellular organizational level intermediate between cells and a complete organ. A tissue is an ensemble of similar cells from the same origin that together carry out a specific function.(Wikipedia) Are all the cells of a tissue of a kind?
In the definition Tissue what is from the same origin?
What you say is true that most of the cells in a tissue are of the same kind. However, as with most rules in biology, there is almost always an exception to these rules. There are only four types of tissues (can be split up into further subdivisions): muscle, epithelial, connective and nervous. Also, a muscle tissue is made up of an ensemble of myocytes (muscle cells). Therefore, the answer to your question would be yes, the cells in a tissue are (if not all, then) almost all of the same kind.
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.
