Is compost a fertilizer

Fertilizer and compost are different items. Neither is better.
Compost is a soil amendment like peat moss, except it has much more. It normally contains many micro-nutrients that common fertilizers do not have. It also has live microbes fungi and bacteria that are needed by many plants to thrive.
Composts may have small amounts of N,P,K (Nitrogen, Potassium & Potash) fertilizers within it, but it depends on the source material of the compost.
Soil amendments change the structure of the soil so roots can grow better and clay soils may drain and sandy soils may hold moisture.
Fertilizers may be from chemical or organic source. They do not change the soil structure or the moisture holding capacity. Fertilizers simply supply the most needed nutrients for optimum plant growth.
For maximum plant growth and strength plants need both compost and fertilizer.
Returning the unused part of plants to the soil via compost maximizes the availability of the nutrients that your plants need and better simulates natural growth conditions.
"The Compost Guru"