Data Warehouse. SQL engine that is much bigger than the databases of yester-year. Their size and scalability give you capabilities that DBAs of a MS SQL dB wouldn't necessarily allow you to do, but think "wow, that is a big database!"
Data Lake. Now your database is stored in blob storage (which is like CSV files on your computer) - and the blob storage is HUGE (like hundreds of Terabytes or larger). Also, you store unstructured data, too. So: pictures, JSONs, raw HTML. Whatever
Data Lakehouse... do you mean Delta Lake? This is a made up word from Dara Bricks. Take your Data lake, and slap a SQL engine on top of it, and add in some marketing slang ;)
Data Mesh. THIS is more about organizations than infrastructure. Imagine a Data Warehouse or Datalake. Now find 5 key stakeholders around your company. Let each of them have a playground in your warehouse. You drop the data into one zone, then they copy it, transform it, and share it in their zone - but they have to play by your rules. Bam. Data Mesh