It depends on the contest, the campaign, and the circumstances. Voter registration data is available upon request from every U.S. state elections authority as well as from every U.S. county that administers elections. This data is what Democratic state and county parties use to cultivate their databases. These databases are then made available to Democratic campaigns.
Postcards to Voters uses voter registration data that is originally created, maintained, updated, and furnished by the state and county elections authorities. Sometimes, the data comes directly from them. Sometimes, it comes from a state or county Democratic party or a campaign committee. But, in most every case with fewer than a handful of exceptions, it comes directly from the campaign.