What does the word 'tub' mean in the phrase 'tub of lotion'?
It's a container.
Tub would be used to describe a container larger than a jar but smaller than a bucket.
Lotions usually don't come in tubs. It's too liquidy.
Butter, lard and soap might come in tubs. That kind of container is large, round, short and wide, with a large top.
There was a time when a bath was an instance of bathing (with no concrete sense). If you wanted to refer to the container you said 'bath-tub'.
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