This is a very good point, a lot of people are totally confused about these two things (either unintentionally or deliberately !) and they confuse others. Those who need a visa to come to DR are in a totally different category to those who do not - DR gov is also very sensitive towards that lot, due to economical situation or whatever other reason, and has placed a visa requirement for their entry. Even westerners who get a visa for work, study or anything else (perhaps even a tourist visa) will have a visa and a stamp on their passport that has an expiry date. You will get in a lot of trouble in DR (or any other country for that matter) if you are caught in the country past that date - it is 100% explicit on your passport that you are breaking the law and your terms of stay.
Now tourist entering the country without a visa and get a stamp in their passport with no expiry date and a big fat sign with a schedule to pay exit fees depending on how long you stay - well, have fun and enjoy your stay for as long as you like... ! lol