Same thing. ADSL is a type of DSL, as is SDSL, ADSL2, ADSL2+, VDSL, RADSL, HDSL, IDSL etc..............
A "DSL" router does not exist (typo's aside).
As for the original question it all depends on type of DSL and ISP. It's better to try and get a router that use's the same internal chipset as those used in the DSLAM's your line is tied into.
As an example Easynet (Sky, Ukonline) use Conexant Argon chipset's in their DSLAM's and when I was taking part in the UK trials of ADSL2+ a couple of years ago we tried ALOT of router's. Billion's 7402 range (using Argon chipset's) were noticably superior to your Netgears, linksys, Actiontecs etc