Are libre office and open office the same company?

libre office and open office?

No. Neither is even a company - they are open source projects governed by organisations.

LibreOffice is community-driven and developed software which is a project of the not-for-profit organization, The Document Foundation. (source)

Apache OpenOffice is both a product and an open-source project. Both have been in existence since October 13th, 2000. 1.0 (the original name, pre-Apache) was released on April 30th, 2002. (source)

More details on the history of LO and how it relates to OOo/AOO on the Wikipedia page. The Wikimedia graphic illustrating the StarOffice timeline is also interesting.