Most gold ever owned

The difference between Most Gold Ever Owned and Total Gold Acquired (q.v.) is that MGEO counts all sources of money while TGA measures money gained by some quests/AH/Vendors only. If a person sends money to a toon via the mail it will not increase their TGA but can increase their MGEO.

Example:

Character One has TGA of zero and MGEO of zero.
Character Two sends Character One 100g.
Character One will now have a MGEO of 100g but their TGA will still be zero.

Another Example

Character One has TGA of zero and MGEO of zero.
Character Two Sends Character One a ring worth 5g and Character One vendors it.
Character One will now have a MGEO of 5g and their TGA will be 5g.

It's also important to note that TGA is iterative and MGEO is not.

Another Example

Character One has TGA of 100g and MGEO of 100g but their current gold is zero.
Character Two Sends Character One a ring worth 5g and Character One vendors it.
Character One MGEO will remain at 100g but their TGA will now be 105g.