Market size
Market size asks how much activity exists in a defined market, period and geography. The definition should state what is included and whether the measure is value, volume or another unit.
Market share
Market share asks how much of that defined market belongs to a company or group. It depends on the same market boundary and on evidence that may not be equally available for every participant.
Why the difference matters
A large market can contain a small share for one company, while a high share in a narrow segment does not describe the whole market. A clear report keeps the measures separate.