The claims of two invention patents filed on the same day are partially the same, is that all right?

Yes, as long as they are not exactly the same technical scheme, they can all be declared at the same time. Patents look at the whole, not one of them.

The patent law provides as follows:

Article 31 An application for a patent for an invention or utility model shall be limited to one invention or utility model. Two or more inventions or utility models belonging to a general inventive concept may be filed as one application.

An application for a patent for design shall be limited to one design. Two or more similar designs of the same product, or two or more designs of products used in the same category and sold or used in sets, may be filed as one application.