Hello,
fouquet, thanks for the comments.
zazy, thanks for posting the answer (which is correct

.
To explain further, this is by design since Google can synchronize multiple numbers of the same type and Thunderbird cannot without gContactSync. gContactSync ignores the actual names of the phone number fields in Thunderbird and instead adds types (Work, Home, Mobile, etc) to make it match Gmail, and improve the address book IMO.
I do see why it can be a problem after disabling or uninstalling gContactSync, or even when using another sync app with Thunderbird. I'd be happy to explain how to use the new phone fields and types to any other extension author if necessary. I filed
Bug 20962 for looking into this, but I cannot make any promises yet.