"Difference between maximum frame size and MTU"
Possibly worth a read, Wiki's MTU.
In short, the Wiki article maps MTU to L3, so for standard sized Ethernet, MTU is 1500. L2 frame size, to hold a L3 packet of 1500, needs a frame size of, at least, 1518 (as you too noted). BTW, frame overhead can be even larger with VLAN tags and or MPLS tags, yet MTU for those would still be 1500. (This is also addressed by @MHM Cisco World's reference.)
Usually, with most media, at the time interfaces are specified, maximum frame size is "cast in stone". Ethernet, though, as it continued to "evolve", with changes like VLAN tags and/or MPLS tags required interface hardware to handle larger frames. Further Ethernet has "evolved" with non-standard Jumbo frame size support.
Once you get into Ethernet frames larger 1518, you're into giant frames, which, being larger than the standard, are considered defective, and dropped. Yet, with things like VLAN tags, etc., those frames might be acceptable to a Cisco interface, as Cisco has defined baby giants, i.e. frames 1519..1600 bytes. I.e. these frames might not be dropped; additional device configuration might be needed to allow.
In the world of jumbo Ethernet, many giant frame might be acceptable; again additional device configuration might be needed to allow.
In this (old) reference, Troubleshooting Baby Giant/Jumbo Frames in Catalyst 4000/4500 with Supervisor III/IV, you might further understand some of the evolution of Ethernet.
In regard to your questions:
Are max frame size and MTU the same, no, as (hopefully) explained above.
"As in, if i specify a MTU of 4000 bytes does that mean a frame has to be larger than 4000 bytes for the error count to change?"
Maybe. Once you get into jumbo size, as they are non-standard, there's no expected/guaranteed behavior.
For example, I've seen some devices that will allow you to set a jumbo size to whatever size you want, up to the maximum jumbo size the device supports. On other devices, enabling jumbo size requires setting it to its maximum.
Without knowing the particular hardware and IOS running (and without direct experience) I could not predict how error counts may, or may not change, as you change MTU. Another reason I provided the (old) reference I did, is to show, even back in 2005, dependencies on actual hardware being used and IOS version being used.
Personally, I would expect as you increase MTU, giant frames covered by the increased size would no longer be considered giants.
