Terminology is an interesting aspect! People use the same terms but they do not always have exactly the definitions for them
You are, of course, right that a good trading plan is also necessary, but a "trading strategy" as you mentioned earlier, in my definition, includes both a trading method and a trading plan. In fact, one could maybe say that a trading strategy in its broadest sense also includes risk and money management.
Another term which is used even more loosely is "percentage gain" as a measure of profitability. Percentage of what exactly! If it is percentage of account balance then it is totally arbitrary and meaningless and a totally useless yardstick for comparative purposes since the balance traders retain in their accounts is entirely a personal matter beyond the minimum to cover trading margins and buffers. To measure monthly profit as a percentage of account equity means nothing - but it is quoted all the time!