It can be a little confusing. A fossil is any evidence of life that has been preserved in rock. So fossils include not just organisms themselves, but also the burrows, marks and footprints they left behind. Fossilization is the name for a number of processes that produce fossils. One of those processes is mineral replacement. This is common in sedimentary and some metamorphic rocks, where a mineral grain may be replaced by material with a different composition, bur still preserving the original shape.
When a fossil organism is subjected to mineral replacement, it is said to be petrified. For example, petrified wood may be replaced with chalcedony, or shells replaced with pyrite. This means that out of all fossils, only the creature itself could be fossilized by petrification.
Scientists don't use the word "petrified" much. What we call petrified wood, they'd rather call fossil wood. But "petrified" has a nice sound and I like to hear it. It sounds right for a fossil of something familiar that looks lifelike (like a tree trunk).