Though often confused as two different entities, there is no difference between a Condominium and a Strata unit.
Why Use Different Terms?
The term Strata was first adopted in Australia as a means to designate a new form of building ownership we now commonly refer to as Condominiums. On the other side of the hemisphere British Columbia was also experiencing this new type of ownership and adopted much of the same legislation and terminology as their Australian counterparts. Unfortunately this terminology would not catch on with the rest of the world.  Australia and British Columbia are the only two locations that utilize the term Strata. Everywhere else refers to them as Condominiums. Cooperatives are another form of a Strata though have different conditions involved. Please refer to the links for more information.
The official term for strata is Freehold Strata. Though just as condominiums are often referred to as condos for simplicity, Strata is more commonly used in place of Freehold Strata for the same reason. Strata is defined in the Province of British Columbia, as a form of ownership governed by the Strata Property Act (1998).
There is contextual meaning for using Strata to describe what everyone else refers to as Condominiums. Strata is a plural form of stratum, which means layers.
This is why the Australians adopted this term, they were referring to the layers in which Condominiums are built on top of each other.
Other uses of the word strata have can be found in geology to describe layers of rock and in social sciences to describe social classes. 
Leasehold vs. Freehold
Freehold is a term referred to when the property being managed is owned as opposed to leased. In the case of condominiums, a freehold strata is then the representative council for a building that is collectively owned by the residents that live there. The maintenance and upkeep of the building(s) is payed for through condominium fees. Property taxes for the building are incurred directly by the owner of each unit. A freehold strata council then serves as the owner of the building and its property by making decisions to best preserve the value of each owners investment while providing services that make the lives of residents as easy as possible. The most important aspect of a freehold strata is that since they have ownership over the building(s) they manage they will have an indefinite tenure. 
Leasehold acts under the same guise as freehold only their tenure to a property is limited to the number of years in the agreed upon lease. Once the lease is up, a council can try to extend the lease or the owners of the building may decide to redevelop the building or the site that the building is on. Leases are more common for older structures whose property has grown in value exponentially over its years of existence. In most cases these buildings are in or near downtown or other gentrified areas of a city and its property has outgrown the value of the building. By imposing a lease, owners of these properties can keep the buildings occupied while while keeping their options open to either redevelop or sell to a company that is willing to do so. Due to this uncertainty, leasehold properties are often much less expensive than freehold strata units.