I don't know how they do it elsewhere, but in the US most of the time trade paperback is an alternative to hardcover -- either it comes out as one or the other but not both. Very, very rarely there is a hard cover and then a trade paperback, for books that are so popular they think it's worth while to sell them in all three formats.
Most of the time the gap between hardcover/trade paper and mass market is roughly a year, although there are always exceptions, and with series books I think it partly depends on how soon the next new book is coming out.