Cost of Revenue and Customer Acquisition Cost are both different metrics. COGS is used in manufacturing in order to peg inputs to a per widget basis. Cost of Revenue gets used in tech because per customer costs are both a bad way to measure it and likely to be fractions of cents.
Customer Acquisition Cost gets used in subscription businesses to measure sales and marketing performance. It can be relevant alongside COGS if you're manufacturing the thing you're selling subscriptions to, but that's kinda rare.
I think "COGS" as discussed here would probably be a rollup of both? Not sure; while I've been in orgs where the cost center/profit center distinction was made, I haven't run into a situation where COGS was a metric I saw used.