Not necessarily. In many cases they mean the opposite, at least in UK usage. Let's say that Mr A ( the landlord) owns a property and Mr B ( the tenant) lives in that property and pays rent to Mr A. In that situation, Mr A is renting the property to Mr B, and Mr B is renting the property from Mr A. As you can see, the verb 'rent' can describe both sides of the transaction, depending on the preposition you use. You can also say that Mr A is letting the property to Mr B, or in the passive form, that the property is let to Mr B. The verb 'let' only works in one direction. It is the landlord who does the letting.

They mean essentially the same thing. Around here, you often see signs "to let" on commercial property and "for rent" on residential property, but in both cases, you sign a lease and make a monthly payment to acquire the use of the property.