@Mauro ********
What prompted me to respond to your original post was your assertion that driving your own car was more "messy", whatever that means.
That couldn't be further from the truth. By far the most straightforward way of entering Malaysia from Thailand is by private car. Its easier and more convenient than traveling on foot - now that's messy! Imagine carting your luggage through the border crossing, dodging lines of cars and trucks at a border not made for pedestrians.
However, train travel is available through the Padang Besar border (as well as by car too), while Sadao is where the Hat Yai to Kuala Lumpur bud passes through. Although there aren't many cross border train services, they are aligned such that you can board a waiting train once you're across and in the relatively near future, there are slated to be more cross border services.
Anyway, since most farang won't be driving (as you can tell from reading many of the posts in this forum) it's worth pointing out various travel options and that when someone asks about how to cross the border, assume they'll be using public transportation.