If we are to look at the differences between eternal and everlasting from a biblical standpoint, we might actually end up treating the two words as one because whenever the Bible uses the adjective eternal to qualify anything it also means everlasting. However, eternal simply means lasting forever, something with no end. While everlasting refers to Lasting or enduring forever; existing or continuing without end.
Spotting the difference between the two words can be really overwhelming because the two words can be used interchangeably depending on what you are saying. However, whatever any difference anybody might come up with will certainly be in the context in which the two words are used. Also we can still look at it this way, eternal means something that was in existence, and is still in existence and will forever be existing, while everlasting means something that talks about an endless future.