The structural difference
A business intelligence system starts with a warehouse: data you produced, under a schema you control, that is definitionally correct because it is your record of your own activity. The work is modelling and visualisation, and the hard problems are consistency and definitions.
Market intelligence starts with no data at all. Everything has to be collected from sources that change shape, go down, contradict each other and are owned by other people. The hard problems are provenance and filtering. A dashboard tool pointed at external sources inherits none of the machinery that makes that safe.
Where teams get caught
The common pattern is a team with a capable BI stack assuming it can answer external questions too. It can display external data, once somebody has collected, cleaned and loaded it. That somebody is usually an analyst doing it by hand, monthly, and the resulting dashboard is a picture of the world as it was when they last had time.
The tell is a competitive dashboard with no date on any figure. Internal metrics do not need one, because the pipeline runs nightly. External figures always do.
What each is genuinely good for
Use business intelligence for anything where you own the record: revenue, pipeline conversion, churn, usage, unit economics, forecasting from your own history. It will always be more accurate than anything external, because it is your own data.
Use market intelligence for anything where the answer lives outside: what competitors changed, what the market is hiring for, which regulations are coming, which accounts show signs of buying. No amount of internal data answers those, and internal proxies for them are usually just lagging indicators of something that already happened.
They meet at the account
The one place the two genuinely join is the account record. Your own data says this account exists, is worth this much and has this history. External intelligence says the account just did something. The join is where a renewal risk or an expansion opportunity becomes visible, and it is worth building deliberately rather than leaving to whoever happens to notice.