What must be true of the units in two rates if one rate can be converted to the units of the other rate? In other words, the units of the
first rate are both/all distinct from that of the converted rate, but it still represents the same measurement?

Yes, if we have two units rate and one rate is converted to another, both measurement will still remain the same even after the conversion but the rate will be different.

For example if we want to convert $2 to naira, note that the unit rates for are distinct but after conversion the amount of both money will be the same.

If $1 = #386

2$ = 2×#386

$2 = #772

Hence the measurement of $2 is equivalent to 386 naira even though the rates are distinct (naira and $)

What must be true of the units in two rates if one rate can be converted to the units of the other rate? In other words, the units of the first rate are both/all distinct from that of the converted rate, but it still represents the same measurement?

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What must be true of the units in two rates if one rate can be converted to the units of the other rate? In other words, the units of the
first rate are both/all distinct from that of the converted rate, but it still represents the same measurement?