Is Tencent Health Electronic Health Card the same as the hospital electronic health card?

It's different.

Tencent Electronic Health Card is a medical service card made by the National Health Planning Commission for residents. This service card is bound to the resident ID card, one person and one yard, which is universal in the whole country. The hospital electronic health card is one card for one hospital, which is not common to each other and is only used by the card issuing unit.