Any difference between "at bay" and "under control"?

Question

In the purpose of writing a vivid article, we are always in the hope that we can change our words at different places even the meanings we express are very similar. For achieving that goal, we need to master vocabularies and fully understand their meanings to avoid mistakes.

Back to my question:
I heard BBC new report on radio

[...] his security guards kept the football officials at bay ¹

Here, at bay means under control. So, can I replace "keep something under control" with "keep something at bay" in any sentence? For example:

A: I keep my cash flow under control --- I keep my cash flow at bay
B: I keep every step of shipping progresses under control -- I keep every step of shipping progresses at bay

Is there any difference between those phrases in meaning, in structure or whatever we need to pay attention to?

Answer 1

At bay has at least two senses that are idiomatic or set phrases:

• Unable to come closer; at a distance
• Cornered; unable to flee

For each sense, wiktionary includes two or three illustrative examples; here are two of them:

• In that case the enemy himself could have occupied the defences of Corinth and held at bay all the Union troops that arrived. – Grant's Memoirs, 1886
• Instead of mounted riders following a pack of hounds, it is envisaged that just two dogs will be used to locate a stag and hold it at bay. – Valerie Elliott in The Times, 2004

I suggested in a comment that neither sense means “under control”, and that at bay cannot interchange with under control. It is true that both senses of at bay involve elements of control, in the first case of someone being able to hold off an opposing force, and in the second of someone or something having limited freedom. But in the first sense, the opposing force is not under control; it is free to move about and try other points of attack. For the second sense, the party held at bay may be unable to escape, but if it's a cornered animal, far from being controlled it's likely to be at its most dangerous.