Clans are team game centric, where groups of players battle in "wars" (a collection of team games) that's scored to see which clan is the best at any given map / moment.
There is a ranking for clans you'll find in this forum called "F400" and you'll be able to see each one and their current / historical rankings.
Tribes are 1vs1 and poly game centric (poly is a premium only feature that's a lot of fun). They also play as a group whose total scores are collected to see who wins and also uses the auto tournament feature.
Tribes are under restructuring and is newer and will probably be growing slowly while clans are more established. Tribes don't have a ranking system.
Generally depends on your playing ability for clans, you can get into different clans by posting in recruitment threads or contacting them via PM. The higher ranked ones will be much harder to get into and have higher expectations for your team play. Some may want to see you gain some minimum experience and bronze medals in the catagories of doubles triples and quads games first. Each clan has their own recruitment methods / entrance guidelines. Some may want test games before admittance.
Once in they are a lot of fun and you'll learn a lot