Any use of the database is done using connection. For example the SSMS connect the database using connection string as any other application. Now lets' examine the situation
Option 1: You connect to the database using SSMS
Option 2: You connect to the database using SSMS, and you work to a table on linked server, which mean SQL Server connected the database in the linked server.
what will be faster?!? As Shanky wrote network has big influence in remote connection and this is Normal behavior that using Linked server will be slower even if the Linked server connect to the same server.
Moreover! You need to check all the connection parameters if you want to compare perfomance. It is a very common issue in the C# forum to get questions like: "It is fast in SSMS, but slow in the my application" and usually the only reasone is that
SSMS use different parameters then the default .NET connection dose.
>> "How can I increase the linked server performance?"
We need more information, lot more :-)
First we need to see the linked server configuration (connection string), next we need to see the queries, and we need to understand the used (maybe we have another solution which is better then linked server like OPENROWSET in some cases), and not less important
we need to understand the architecture (is the linked server connect to remote server or local