Not they are not the same. Fixed costs are costs that do not change when you increase or decrease the output. For example, your rent is going to be same if you sell 1000 or 10000.
Relevant costs are costs that you need to take into consideration when you do investment appraisal or when you price your products. Relevant costs include fixed costs and variable costs.
Fixed costs are relevant as long as they are avoidable (if you not go forward with the project). For example, if you are considering expanding your business and you will have to rent another office, this fixed cost is relevant. However, if you want to launch a new product and you will not need to rent new space, the rent that you are already paying is not relevant.