The main difference between a lifestyle and a posed newborn session is the approach to the photography and the way the pictures are captured.
In a posed newborn session, the photographer will typically use a studio setting ( it can also be done at client's home) and will carefully position the baby into a variety of poses. These poses are usually quite traditional and are designed to showcase the baby's features and expressions. The photographer will take a series of photographs while the baby is in these poses and the parents or siblings may also be included in some of the photographs.
On the other hand, a lifestyle newborn session is typically shot in the comfort of the baby's home and is intended to capture the everyday, candid moments of the baby and the family. The photographer will typically capture a variety of candid and natural shots of the baby and the family interacting, playing, and bonding. This type of session is more relaxed and less formal than a posed session, and it aims to capture the real, everyday life of the baby and family.
Both posed and lifestyle sessions can be great to document the arrival of a new baby and both have its own unique pros and cons. Posed sessions are more predictable and the photographer can get very specific type of images, but Lifestyle sessions will have more candid, natural and spontaneous images.
It ultimately comes down to personal preference and what type of photographs you are looking for. It's important to communicate with the photographer and understand their style, so you can make a decision that best suits your needs and expectations.