The main differencees between wraps and slings ect (without writing essays) is a wrap is like a really strong scarf (but purpose weaved) which you literally wrap around you and the baby. There are loads of different ways of wrapping for back and front carry. A stretchy is just that a stretchy carrier that has no buckles or rigid structure. It is perfect for newborns. Check out close caboo to see what I mean.
A sling covers most styles of carrier from ring sling to wraps to mai tei.
Here is a quick summary of some of the choices:
Wrap –these are either cotton or blended with wool or bamboo. Used for traditional wrapping and can be used from birth.
Ring sling – like a wrap but with rings sewn into the end to feed the other end through (tail) and these usually sit across the body. I use mine for quick ups and downs when Ds was learning to walk further.
Mei Tie and Pods – these are more structured – a panel with straps to tie around the waist and body.
Half buckle and reverse half buckle – these either have buckled straps and tie waist or tie waist and buckled straps.
Full buckle - buckles waist and straps. (Ergo baby, manduca, Connecta). These usually have an insert for newborns.
A mentioned earlier, try to avoid narrow based cartiers like the baby bjorn. Althoughthey have an ergonomic out now too.
Check out the TICK guidelines babyslingsafety.co.uk/ticks.pdfHope that helps