[sql] Select from one table matching criteria in another?

I have a similar problem (at least I think it is similar). In one of the replies here the solution is as follows:

select
    A.*
from
    table_A A
inner join table_B B
    on A.id = B.id
where
    B.tag = 'chair'

That WHERE clause I would like to be:

WHERE B.tag = A.<col_name>

or, in my specific case:

WHERE B.val BETWEEN A.val1 AND A.val2

More detailed:

Table A carries status information of a fleet of equipment. Each status record carries with it a start and stop time of that status. Table B carries regularly recorded, timestamped data about the equipment, which I want to extract for the duration of the period indicated in table A.