As Steepsays ASA (Now defunct) and ISO are the same - the numerical values denote the same film speed, or with digital - sensor sensitivity.
There wasn't actually an ISO number in your Minolta days, you're probably thinking of the DIN rating (Deusche Industry Norm) which was a German system running alongside ASA for years. When you bought a film it would have both ASA and DIN ratings on the carton. 400ASA = 27DIN - 200ASA = 24 DIN. An increase of 3 under the DIN rating doubled the film speed. DIN was a crap system and after a big dust up between the Yanks and the Germans, both systems were swept away in favour of the single ISO system we now use which is really still ASA by another name. :wink:
You are right in saying that the higher the ISO the less light you need, but you're wrong in thinking you get a better picture, in fact the reverse is true.. This applies equally to film or digital.
A film is basically just a gelatine strip covered in silver halide crystals which are light sensitive. The only difference between a slow film and a fast one, is that a slow film has very fine silver halide grains, so you need good light to use it, but you get very good enlargements due to the fine grain. With fast film the bigger grains of silver halide catch more light - it's really that simple. The downside is that as you begin to enlarge your iimage that large grain structure becomes visible much more quickly.
With digital we don't have grain, we have pixels, but you'd have to enlarge an image much bigger than 1:1 to see them. The problem we have with digital is image noise. Image noise is that pitting you see in your images, particularly in the shadow areas and in shots taken in low light. The practical problems are just the same as with film and grain. The higher the ISO number the lower the light you'll be able to work in but the penalty is noise in your images. As with film, we get the highest quality images with digital by using the lowest ISO number we can in any given circumstances. Circumstances often force us to use a higher ISO than we'd like. One of the many advantages of shooting in RAW format is that RAW processing software is usually pretty good at filtering image noise out to get the best noise free images you can if you're forced to use high ISO.
It's important to understand that each time you double the ISO number, it's only the equivalent of being able go one stop quicker on your camera. In other words if you were shooting at 100 ISO with your lens wde open at f4 and a shutter speed of 1/30 sec, changing to 200 ISO would only enable you to set a shutter speed of 1/60sec, but that would be a far safer bet for hand holding even with a standard (50mm ) lens. The differences can be that fine sometimes.