From the light wallet REST API spec:
transaction_height = Total txes sent in Monero
scanned_height = Current tx scan progress

These are in contrast to:
blockchain_height = Current blockchain height
scanned_block_height = Current scan progress

But can see here the response for all 4 is always in terms of block height, not tx count

Should be a simple fix, marking for later

Side note: I'm not sure if start_height is correct in monero-lws or in MyMonero, but MyMonero seems to be returning a tx count for start_height rather than block height (monero-lws returns block height). Worth a deeper investigation into this discrepancy I think.