Hi, so I'm quite new at DnD and I wanted to make one of my characters an Eladrin. More specifically a fey eladrin, however I could only find Eladrin Variant. Are they the same? And I also noticed there was a few other types of eladrin, so are they also apart of eladrin variant? 

Eladrin appear in 3 different books, so that might be the confusion. 
The “variant” appeared in the ‘14 dungeon masters guide. Then there are versions in mordenkainen’s tome of foes and also mordenkainen’s monsters of the multiverse. 
The last one, monsters of the multiverse, is the current version.  
By RAW, you can’t be a fey eladrin. Fey is a creature type, and while NPC eladrin are fey, eladrin PCs are humanoid, not fey.

The other types you see are probably the different seasons of Eladrin. As a pc, you can change your season, so I wouldn’t worry about those versions at all.

So, if you want to make an Eladrin character here, you’ll need to either own monsters of the multiverse, or join a campaign where someone shares it with you. Then you can make a humanoid eladrin.

Thankyou! This helps me a lot!