Laser intersatellite links (LISLs) are envisioned between satellites in upcoming satellite constellations, such as the one in phase I of SpaceX's Starlink. Within a constellation, satellites can establish LISLs with other satellites in the same orbital plane (OP) or in different OPs. We present a classification of LISLs based on the location of satellites within a constellation and of LISLs' duration. Then, using the satellite constellation for phase I of Starlink, we study the effect that varying a satellite's LISL range has on the number of different types of LISLs it can establish with other satellites. In addition to permanent LISLs, we observe a significant number of temporary LISLs between satellites in crossing OPs. Such LISLs can play a vital role in achieving low-latency paths within next-generation optical wireless satellite networks.