littleConnie, IMO the 2 different ways are as follows:
Puree - as the name suggests you puree all food and give to your baby by spoon. Most people start off with something quite bland like pear and add baby rice. Not sure why baby rice as it doesn't taste of anything and is like wallpaper paste. Maybe it's used as a filler? You then decrease the smoothness of the puree's so your lo learns how to eat lumps. I would say (and this is a huge generalisation so I apologise in advance) people who like to control and have order will prefer this method.
BLW - you give pieces of food to your lo and it is up to them to pick the food up and put it in their mouth themselves. The theory being, if they can do it themselves then they are ready for food. It also encourages self regulation of their appetites (ie they only eat what they want as they are not having food spooned into their mouth and being made to eat how much we think they should eat, much like bf'ing.) The pro's for blw are self regulation of appetite, no pureeing, and as blw babies tend to be weaned later they can eat a bigger spectrum of foods straight away. If you don't like mess and stress over waste, and not knowing your baby's food intake I would imagine blw isn't for you.
Whatever route you take, your lo shouldn't have any dairy, gluten or wheat before 26 weeks - there may be other no no's as well, but they are the one's I can remember for 6 months. After 6 months they can have dairy, wheat and gluten, but their main fluid intake should not be cows milk. For example having yoghurt and cows milk on cereal is fine, but do do not substitute breastmilk/formula for cows milk.
Hope this helps