Our library system divides age-appropriate storytimes into babies (0-12 months), "Tiny Tots" (12-24 months), toddlers (24-36 months), and preschool (ages 3-6). We also have family storytimes (ages 0-6 or whoever shows up), including evening "Pajama Time" storytimes.
We are flexible about families bringing siblings of other ages along, and it generally works out fine.
Some of us modify the age ranges to reflect crawlers vs. walkers (more or less). Some of us take babies up to 18 months in the "baby" storytime, and lump kids aged 18-36 months all into "toddlers." I tend to steer crawlers (along with the sit-and-marvel babies) to the "baby" storytime, but once they are up and stomping around a lot and trying to hold onto books, invite them to try the "toddler" storytime.
We are not sticklers for these divisions but try to guide families to the storytime that seems to best suit their kid(s). For example, a high-energy, short-attention-span 3-year-old usually fits better into the "toddler" storytime than into the "preschool" one, where stories are more involved and longer.
For us, "storytimes" may include books, stories, songs, rhymes, fingerplays, activities, music and sometimes crafts appropriate for the ages attending. The intent is to share the fun of books and reading and to foster early literacy skills.
(On our web site, storytimes are described thusly: "Introduce young children to books and reading at our fun storytimes. Each week, librarians and specially trained staff adapt stories, songs, and movement activities to match the ages and attention spans of the children attending. Parents learn how to foster early literacy skills to prepare their children for learning to read. Librarians answer questions about books and library services, and teach parents how to interest their children in books.")
For storytimes in languages besides English we don't have the resources to divide by age, so those are all "family" (ages 0-6) storytimes. That tends to work out fine as families typically bring siblings of many ages anyway. We also offer family storytimes for children with sensory integration issues, and we are about to pilot a storytime grounded in the black American cultural experience.