Snapchat still shows Invite for added users. Also, someone I want to add who is in my phone’s contacts list doesn't show up when I go to “Contacts” in Snapchat, and I know they have the app because they use it.
This could happen because those users refused your invite, or the invitation expired. You can simply re-issue the invites again and then see who responds, but that can be easily checked in the Friends list available within your Snapchat application.
For additional information and instructions related to the friend adding procedure, access the following link which leads to the Snapchat's support website: https://support.snapchat.com/en-US/a/find-friends