Both restrict transfers of an ownership interest, and the difference matters commercially.
A right of first refusal requires an owner who has received a bona fide third-party offer to present it to the company or the other owners, who may buy on the same terms. The holder therefore sees a real, priced deal before deciding.
A right of first offer reverses the sequence: the owner wishing to sell must first offer the interest to the holders at a stated price, and only if they decline may it be sold to a third party — usually on terms no more favourable than those offered.
The practical difference is the effect on the market. A right of first refusal depresses the pool of interested buyers, because a third party must spend time and money on diligence knowing an insider can step in at the end and take the deal. A right of first offer is friendlier to a seller for that reason.
Terms that decide how either works in practice: the response period, whether the holder must take the whole interest or may take part, whether it applies to transfers to family or trusts, and what happens if the third-party sale does not close on the original terms — a well-drafted clause requires the process to restart if the price drops.