Firstly, both phrases are very casual. They would be used between two people who know other. Both have the same meaning and are simply confirming what was just said, or read, or seen. Both phrases would usually be preceded by the word "that" e.g. "That seems right". Also, in my opinion, "that seems to be right" is a bit less sure than "that seems right".

The difference between "seems right" and "seems to be right" is subtle and often context-dependent, but they can be used in slightly different ways: "Seems right": This phrase is more straightforward and implies that something appears to be correct or appropriate based on the available evidence or intuition. It’s often used in informal contexts. Example: "The solution you proposed seems right." (This suggests that, based on what you know, the solution appears correct.) "Seems to be right": This phrase adds a bit more formality and emphasizes the process of assessing or evaluating something. It can imply that there has been a consideration or evaluation leading to the conclusion that something is correct. Example: "After reviewing the data, the conclusion seems to be right." (This suggests that, after a more deliberate process of review, the conclusion appears correct.) In most cases, the two phrases can be used interchangeably without significantly changing the meaning. However, "seems to be right" might be preferred when you want to emphasize the evaluation process or add a bit of formality.