The processes that you go through are similar but what happens inside the grain is different.
In base malt there are enzymes and starches. The starches need to be converted to sugars. Some of those enzymes are capable of doing that conversion but need to be activated. Different enzymes are active at different temperature ranges - the ones that convert starch are active between approx 60 and 70 (I think it's around 59 to 72 but not certain). This is mashing.
In specialty malt, the kilning/roasting process will have already activated the enzymes and starches will be converted. In most cases the available sugars will have been 'cooked out' by this process although some crystal malts will still have available sugar etc.
These only need to be steeped (soaked) for colour and flavour - very little fermentables will come out and even a cold steep will work.
Then there are a few malts such as biscuit malt which need to have starches converted for use but cannot do it on their own as they don't contain the right enzymes. They need to be mashed with other base malts.
While the process is similar (soak in water) a steep will work at 50 degrees or 20 degrees whereas a mash will not.