Movement Types
Source Player Core pg. 412
The majority of creatures have a Speed, which is how fast they can move across the ground.
There are other ways to move, such as through the air or underground. Each of these special movement types has its own Speed value. Many creatures have these Speeds naturally, such as a barathu having a fly Speed or a kalo having a swim Speed. The various types of movement are listed below. Since the Stride action can be used only with your normal Speed, moving using one of these movement types requires using a special action, and you can't Step while using one of these movement types. Speeds can be increased or decreased with item, circumstance, and status bonuses and penalties. Penalties can't reduce your Speeds below 5 feet unless stated otherwise.
Switching from one movement type to another requires ending your action that has the first movement type and using a new action that has the second movement type. For instance, if you Climbed 10 feet to the top of a cliff, you could then Stride forward 10 feet. In some cases, the GM might rule otherwise, especially if you're moving a very short distance using one of the types of movement.
There are other ways to move, such as through the air or underground. Each of these special movement types has its own Speed value. Many creatures have these Speeds naturally, such as a barathu having a fly Speed or a kalo having a swim Speed. The various types of movement are listed below. Since the Stride action can be used only with your normal Speed, moving using one of these movement types requires using a special action, and you can't Step while using one of these movement types. Speeds can be increased or decreased with item, circumstance, and status bonuses and penalties. Penalties can't reduce your Speeds below 5 feet unless stated otherwise.
Switching from one movement type to another requires ending your action that has the first movement type and using a new action that has the second movement type. For instance, if you Climbed 10 feet to the top of a cliff, you could then Stride forward 10 feet. In some cases, the GM might rule otherwise, especially if you're moving a very short distance using one of the types of movement.
Speed
Source Player Core pg. 412
Most characters and monsters have a Speed statistic that indicates how quickly they can move on a solid surface. This statistic is referred to as land Speed when it's necessary to differentiate it from special Speeds.
When you use the Stride action, you move a number of feet equal to your Speed. Whenever a rule mentions your Speed without specifying a type, it's referring to your land Speed.
Hover: Some creatures, such as barathus, have a land Speed that represents how fast they can move while hovering within 5 feet of a solid surface. Hovering creatures don't count as flying but might be able to avoid certain types of difficult or hazardous terrain, at the GM's discretion.
When you use the Stride action, you move a number of feet equal to your Speed. Whenever a rule mentions your Speed without specifying a type, it's referring to your land Speed.
Hover: Some creatures, such as barathus, have a land Speed that represents how fast they can move while hovering within 5 feet of a solid surface. Hovering creatures don't count as flying but might be able to avoid certain types of difficult or hazardous terrain, at the GM's discretion.
Burrow Speed
Source Player Core pg. 412
A burrow Speed lets you tunnel through solids. You can use the Burrow action if you have a burrow Speed. Burrowing doesn't normally leave behind a tunnel unless the ability specifically states that it does. Most creatures need to hold their breath when burrowing, and they might need tremorsense to navigate.
Climb Speed
Source Player Core pg. 412
A climb Speed allows you to move up or down inclines and vertical surfaces. Most creatures need to succeed at Athletics checks to Climb, but if you have a climb Speed, you automatically succeed and move up to your climb Speed instead of the listed distance.
You might still have to attempt Athletics checks to Climb in hazardous conditions, to Climb extremely difficult surfaces, or to cross horizontal planes such as ceilings. You can also choose to roll an Athletics check to Climb rather than accept an automatic success in hopes of getting a critical success. Your climb Speed grants you a +4 circumstance bonus to Athletics checks to Climb.
If you have a climb Speed, you're not off-guard while you're climbing.
You might still have to attempt Athletics checks to Climb in hazardous conditions, to Climb extremely difficult surfaces, or to cross horizontal planes such as ceilings. You can also choose to roll an Athletics check to Climb rather than accept an automatic success in hopes of getting a critical success. Your climb Speed grants you a +4 circumstance bonus to Athletics checks to Climb.
If you have a climb Speed, you're not off-guard while you're climbing.
Fly Speed
Source Player Core pg. 412
As long as you have a fly Speed, you can use the Fly and Arrest a Fall actions. You can also attempt to Maneuver in Flight if you're trained in the Acrobatics skill.
Wind conditions can affect how you use the Fly action. In general, moving against the wind uses the same rules as moving through difficult terrain (or greater difficult terrain, if you're also flying upward), and moving with the wind allows you to move 10 feet for every 5 feet of movement you spend (not cumulative with moving straight downward). For more information on spending movement, see Tactical Movement.
Upward and downward movement are both relative to the gravity in your area; if you're in zero gravity, moving up or down is no different from moving horizontally.
Wind conditions can affect how you use the Fly action. In general, moving against the wind uses the same rules as moving through difficult terrain (or greater difficult terrain, if you're also flying upward), and moving with the wind allows you to move 10 feet for every 5 feet of movement you spend (not cumulative with moving straight downward). For more information on spending movement, see Tactical Movement.
Upward and downward movement are both relative to the gravity in your area; if you're in zero gravity, moving up or down is no different from moving horizontally.
Swim Speed
Source Player Core pg. 412
With a swim Speed, you can propel yourself through liquids with little impediment. Instead of attempting Athletics checks to Swim, you automatically succeed and move up to your swim Speed instead of the listed distance. Moving up or down is still moving through difficult terrain.
You might still have to attempt checks to Swim in hazardous conditions or to cross turbulent water. You can also choose to roll an Athletics check to Swim rather than accept an automatic success in hopes of getting a critical success. Your swim Speed grants you a +4 circumstance bonus to Athletics checks to Swim.
Having a swim Speed doesn't necessarily mean you can breathe in water, so you might still have to hold your breath if you're underwater to avoid drowning.
You might still have to attempt checks to Swim in hazardous conditions or to cross turbulent water. You can also choose to roll an Athletics check to Swim rather than accept an automatic success in hopes of getting a critical success. Your swim Speed grants you a +4 circumstance bonus to Athletics checks to Swim.
Having a swim Speed doesn't necessarily mean you can breathe in water, so you might still have to hold your breath if you're underwater to avoid drowning.