Well, the values in the book assume you are moving, and so did I. You would definitely never write down a combat action with the implied meaning of "but this is harder if you are moving", because you are almost always moving. If you think DC 15 is too easy (I do not) then make it higher. Remember that the ride check of a person lightly trained would on average be +0 to +4, so if your intuition says that something should work about half the time for someone conversant in that skill (aka, a very bad success rate and highly risky in combat), DC 15 is the right place to go. If something could only be achieved with great luck and stupendous training (aka, nothing that ever happened historically, but something that might be in a legend that COULD be true, once), then it might only have a 25% chance of success if someone is highly dextrous and trained- a DC 30 would be appropriate there. A DC 20 is something that could be achieved pretty rarely and might be selected by a normal person when the alternative is death, etc. Certainly anything that happened historically with trained soldiers should become a sure thing to a fully trained E6 character.
In any event, if you want to differentiate moving and stationary, moving would be the default and you'd give a bonus for stationary (bonus to roll or lower DC). Galloping (run action) would be a different story, and I would suggest -4 as that seems to be the sort of penalty such a state implies to other values.
The action matrix is fucked up because there's two kinds of free actions. By the book, a free action can be done whenever, whether it is your turn or not, such as speaking, and the DM can put limits as to how much can be done in a round (you could shout instructions but not recite a sonnet). But later documents usually mean free action to mean "unlimited, but only on your turn".
The table is here but:
http://www.d20srd.org/srd/combat/actionsInCombat.htmBasically our version is:
Not an action- Events that take place as PART of another action.
Free action (whenever)- actions such as speaking, thought, certain mental or vocal abilities, dropping an item or weapon, and some state based action such as reacting to forces like gravity.
Immediate Action- A very fast action that can be used at any time. You can only use one swift or immediate action per round. We've always played that you get back this "temporal token" at the beginning of your round.
Swift Action- A very fast action that can be taken during your turn. You can only use one swift or immediate action per round, so if you use a swift action, you can't use another, or an immediate action until the beginning of your next turn.
Free Action (your turn)- You can only do these on your turn, but you have an unlimited amount of them, subject to DM discretion.
Five Foot Step- If able to move and you have a movement speed of five or more, you can, during your turn, take a five foot step if you take a full round action or a standard and a move equivalent action.
Move Equivalent Action- Takes the same opportunity cost as a move action, but does not move you.
Move Action- Takes a meaningful amount of your time to use some manner of physical locomotion. You cannot take a five foot step in a round where you use a move action unless that move action is some kind of bonus.
Standard Action- A normal amount of time that represents the bulk of a round.
Full Round Action (this round)- Consumes your full round. You can still take a five foot step before, during, or after. Your effect takes effect immediately. Example: Full attack.
Full Round Action (next round)- Consumes your full round, and you continue doing the action until the beginning of your next turn. If stopped or interrupted, your action is partially completed, incomplete, or cancelled, which may result in its negation (such as spells).
Two of these are not at all friendly (the two free actions and the double meaning of full round action). Additionally, the game designers made some odd choices- by the book, a quickened spell is a free action that you can do once per round, meaning you can take the effect whenever you want, and it doesn't interfere with any other actions. Later the swift action was introduced, and that stayed the same, but then at some point the swift action nomenclature was used to describe a quickened spell. We've played them as immediate actions since quick and immediate were launched.
The shittiest part is that the quick and immediate actions were launched with the psionics handbook, where they saw very light usage, but this meant that many never saw the source. They got rolled into some rules errata, but the main rulebook still doesn't talk about them (the SRD does, but that's literally edited in). They also got really heavy usage in later rules, and in 4ed the actions are "minor, move, standard". The heaviest usage is in 9swords, where a ton of martial techniques are swift actions and a few immediate, and some of the later books offer decent swift and immediate spells, many of which last only a single round or have a greatly reduced effect.