Difference between UL and Non UL PCB
As mentioned in comments, UL marking requires that the components are UL certified. Or, in this instance, UL recognized which means they are components meant to be used as a part of UL listed product. Difference between UL listing and recognition is that the latter is a relatively lightweight process.

You don't need to use UL recognized parts to get UL listed and using UL recognized parts does not mean your product is UL compliant by default. Usually UL recognition includes some caveats on how the parts need to be installed, assembled, used etc. 

In order to "get" that UL recognized marking, you have to fork a lot of money and effort towards UL. They're essentially a tax towards electronics in US market. Fortunately there are other certificates that are acceptable (CB by TÜV) so UL does not get away with murder like it once could. Instead it just gets a small fine and a bit of community service. 

Similarly to get UL listed means you provide your product samples to UL who charges you a lot of money and gives (or not) a certificate your product isn't going to electrocute someone, catch fire etc. This is similar to the CE marking except that consumer goods CE marking can be done by "manufacturer's declaration", which you can pull out of thin air. But that may mean jail time if your product kills someone or burns their house down. For regulated fields such as medical and industrial, formal CE testing with recognized organisation (notified body) is required. For medical devices you also have to have a quality system which is audited regularly.