Bless him, but SZ means 'ascent' shoes, sometimes also called approach shoes. In other words shoes to wear in the walk up to the base of a mountain, i.e. anywhere other than fell walking. They're great in summer as they're generally lighter and more breathable than 3 season boots.
These generally tend to have a low to mid ankle cuff which may be a problem if walking on muddy paths, but do now tend to come with Goretex linings although this doesn't stop water/mud coming over the top. However GTX pushes the price up, so if you're anticipating walking in a lot of mud, my personal view is that I'd rather have a pair of simple design leather 3 season boots which are much easier to clean. You won't find much price difference between GTX approach shoes and some leather boots, although as SZ says, you may find sale items around.
I tend to wear approach shoes as general outdoor shoes, as they usually have cushioned soles so I find them far more comfortable than normal shoes, and as SZ says, they look like a pair of trainers. I used to find that after a long walk, wearing a pair of normal shoes with no cushioning was like walking on a stony beach with no footwear, so have now been wearing approach shoes as a matter of course for many years. Because they're not trendy (sometimes silly) designs, they tend to be cheaper than trainers although often far better quality.
S.