Most behaiviors which we could call typical of animals and we would expect in many advanced species have evolved convergently in insects and other small invertebrates. Advanced sociality, kin recognition, territoriality, male to male combat, mate guarding, pair formation, parental care, altriciality of young etc. Then is there any real difference about these animals and the larger, supposedly more sophisticated mammals?

as you say these are examples of apparently convergent traits that presumably happen because they provide a selective advantage (to the individual and/or the "herd"). In some cases similar gene pathways or networks may underpin them even in very different species. Once again words like "sophisticated" when used to compare different species is problematic.