Is the timing of developmental milestones the same for all children?

Good question. Developmental screens/ assessments are based on biological development, the age ranges during which typically developing children reach certain milestones. Clearly, there are cultural, environmental and socioeconomic factors ( such as poverty, amount if child-directed language a parent gives, parenting style and expectations) that impact a child's development.
No. No, not all children attain developmental milestones at the same time. Don't worry if your child takes an extra month or two to babble his first words, or take her first steps. All babies are different and attain their milestones at their own speed. You should worry if several months go by without attaining a specific milestone, or if your child appears delayed in attaining multiple milestones.
No. Some children reach the milestones earlier while others may reach them later. Try not to compare your child to others. Your pediatrician will do a developmental screening at each well child visit and will address your concerns. If your baby is significantly delayed, further evaluation may be needed.