There are many types of Speed up in Gradius and Salamander. Here are the following:

Speed up: The most references in gradius games

Speed Down: Allows vic viper to reduce 1 speed or 5 speed.

Hyper Speed: (ONLY in Life Force JP, Salamander Prize version) Allows vic viper and lord british to use 2 speed ups at ONCE.

Turbo booster: This was used in Gradius Gaiden to prevent them from sucking from the Black hole in stage 7