MTE is essentially hardware-accelerated AddressSanitiser[1].
To expand a bit: 16-byte chunks of memory can be associated with a four bit tag. Then you steal four unused high bits from your pointers to store a tag value. When memory has a tag, a pointer used to access it must have the matching tag in its high bits. Your malloc implementation can then assign a different tag to adjacent allocations and any overflow into an adjacent allocation will have a mismatched tag and will trap. Likewise, change the tag on free and an attempt to use the pointer after the allocation has been freed will trap.
Of course, this doesn't come for free. Four bits per 16 bytes means a 3% increase in memory needed for tagged memory, hardware overhead for checking tags on memory accesses, and software overhead of setting/changing/clearing tags as necessary. This overhead is low (Apple shipped this in flagship hardware a year ago and nobody's complaining about performance there) but not zero, and an implementation with poor performance could be a real problem.
No MTE and AddressSanitizer are implemented completely differently under the hood and catch different kinds of memory bugs.
MTE tracks provenance of pointers which means it catches bugs where a valid pointer derived from one allocation is used to access another allocation. Provenance is indicated by a fixed number of tags available. So there’s a 7% chance of not detecting an occurrence of a memory bug.
ASan is implemented differently: it adds red zones next to allocations. In theory it could have a false negative if a pointer jumps over the poisoned region. But it works well for stack memory in addition to heap memory. MTE doesn’t protect your stack allocated objects.