In my opinion a TRI is a lesser rating than FI, a TRI can only do type ratings on relevant type. The FI can do much more incl. multi engine type ratings provided certain experience requirements are meet.
See:
"JAR–FCL 2.320C FI(H) – Privileges &
Requirements.
The privileges of the holder of FI(H) rating (for
restrictions see JAR-FCL 2.320B) are to conduct
flight instruction for the issue, revalidation or
renewal of:
(f) A single-pilot multi-engine type rating,
provided that the FI(H) meets the TRI
requirements of JAR-FCL 2.330B(b) & (d), and
JAR-FCL 2.330E(b);"
Both an FI & TRI need to have at least 500TT and 100hrs on multi engine helicopters to instruct in them as well as demonstratehis ability to instruct on the ME type to the authority.