Artar, the discussion of DC vs AC motors is a lengthy one.
Primarily, it has to do with AC "cogging" vs DC "non-cogging" regarding the way the motors work.
"Cogging" is the result of the motor behavior when the individual poles of the motor pass the magnets. A 4-pole motor will have a "surge and lag" effect as each pole passes the magnetic parts of the motor that can be noticeable. AC motor makers have increased their number of poles to reduce this effect, and commonly now use 24-pole motors. The effect is reduced, but not entirely gone.
AC Sychronous motors use the AC line frequency(60Hz) that is generated by the power company to use as a speed reference that keeps their motor speed "constant", similar to an electric clock. Since it locks on the line frequency, and not the voltage level, it can remain constant even during fluctuations of voltage. It is a commonly used type of drive for most of the lower cost turntables, and is even used fairly commonly in expensive turntables.
DC motors do not have a cogging effect, but since there is no "line frequency" in DC, there is no reference to "lock" on the speed like an AC motor does. DC motors are speed controlled by the voltage level. So, the DC motors must have some kind of controller, or the TT will constantly undergo minor slowing as you play the LP, due to drag forces. The "best" kind of controller for the DC motors is a subject of great debate.
Obviously, a "quartz lock" or other "hunting" type of controller that uses a strobe as a reference can have the effects of quick speed up/slow down known as "hunting". This is not good. Teres has developed a controller which uses strobe reference on the platter, which senses variations and applies corrections in a very slow manner, which is not really audible. Some may argue this and claim it is audible. The other method is to use a relatively non-referenced controller which sets speed as a constant, and hopes that nothing really slows the platter down along the way. Any slowdowns with this type of controller will be additive all along the side of the LP being played. Some will argue that this is not noticeable, but others say it is. In either case, the platter momentum is critical to the controller not having to make corrections, or not slowing the platter down during play. Neither of these systems is perfect, and the AC synchronous system is not perfect. Nothing is perfect. Since the ear is most senstive to minor speed variations occuring in a rapid manner(flutter), we strive to minimize flutter, but the methods we use may result in more slower variations(wow). "Wow"(in small levels) is less noticeable to the ear. So, the DC motor application is used to provide the smoothest results in flutter, but may have a bit more wow, or a bit more gradual slowdown, depending upon the type of controller used. In addition, belt stretch and rebound, belt slip, and other things may enter into the equation. It is a difficult engineering task to get close to perfection in this area, and there is no solid consensus on the best method to use. However, it is generally conceded that a well implemented DC motor can sound better than an AC synchronous. The individual TT makers use their ideas of what the best method is, and the user must decide which he prefers sonically. Most of the best units are very very good, and will not intrude into the listening experience noticeably.
Regarding the question about platter mats, the Teres is not designed to use a mat, and should be played "bare". If you want a better platter than the acrylic because of the reflected resonance issue, then stepping up to the next higher level of platter will be useful, not adding a mat.
However, be aware that there is no "perfect" platter either, and it remains a choice of imperfections which is most acceptable to you. There are sonic issues with every single type of platter you may select.
In fact, every single choice you make as an audiophile will have plusses and minuses. It is up to you to select equipment which has the plusses in the areas of most importance to you, and has the minuses in the areas of least sensitivity to you. This is the crux of assembling a satisfying system that will meet your needs as a listener, and it is also why there are so many different ideas of what is "best".