Every poll you create is saved in your poll library. You can place any poll on another page or post, and it keeps all of its votes.
The poll appears with its full history, and new votes are added to the same results.
If the same poll is shown on two pages, both pages feed one set of results. For more on this, see Can I use the same poll on more than one page? and What is the difference between creating a new poll and selecting an existing one?
You can also give a poll a category from the block settings. The category is saved straight away and applies to the poll everywhere it appears. See Organizing polls with categories.