The reason, I believe, that many people think that aldehydes smell soapy is that many soap fragrances contain a lot of aldehydes. They work really well in soap bases, and many of the early soap brands (such as Lux and Camay) used a cheapened, modified version of a Chanel 5 type.
An aldehyde is a type of organic chemical ( a chemical based on chains of carbon atoms), and there are many used in perfumery. Vanillin (the major component of Vanilla) is an aldehyde. The chemicals responsible for the smells of Cumin and Cinnamon are both aldehydes. As you can see these three smell very different from each other.
What we mean when we describe a smell as being "aldehydic" is that is smells of a sub set of aldehydes called "Aliphatic Aldehydes". These consist of a long chain of carbon atoms with the Aldehyde group (the special arrangement of atoms that all aldehydes have) at the end. So we have ALdehyde C8 (a chain of eight Carbon atoms with the aldehyde group at the end), C9, C10 and so on. They all smell slightly different, but all can be described as having a fatty, waxy, although sparkling odour. Aldehyde C8 and C10 are found at fairly low levels in citrus oils (you don't need much as they are very strong) and have a slight citrus odour (C8 more Orange, C10 more Lemon). Aldehyde C11 (in fact there are two Aldehyde C 11, but don't worry about that at this point) start to smell less Citrus and more floral (think of the sharp green part of Rose or Lily of the Valley). There are also two Aldehyde C12s. One is similar to the C 11 but somehow heavier, whilst the other (called Aldehyde C12 MNA) smells woody and Pine like.
Chanel 5 is the classic Aldehydic fragrance, but as has been pointed out, there are may others. Aldehydes are used in many fragrances, at various concentrations, to provide a lift and sparkle without necessarily being obvious. They are useful when making fragrances for other applications (such as soap) as they are able to lift a fragrance so that the base odour is covered.