The difference between the two is focus.
Art focuses more on the development of the artisan, his/her ability to perform the art in selected mediums, and the depth that the artist understands their internal world AND how the art links to the world around them. "Poetry is everywhere", "Everyday Martial arts..." and such phrases. The philosophy behind 'art' isn't always as clinical as tactical training.
Tactics and tactical sciences are about application and outcomes. It deals with understanding a systemized approach to reading and reacting to a given situation, sizing up your assets and those of your opponent's and forumating the best response: whether by accessing a 'canned' response (immediate actions) or by making something up on the spot (based on prior training and ingenuity of course).
"tactics" for a military leader will be different than those applied by an individual simply because the assets are different, the 'mission' may be different and the 'enemy' may be different, but the same principles will apply with a given 'philosophy' of tactical theory.
"Hard" styles are very rooted and rely on a solid stance, power deliver and intestinal fortitude of the user to gut out the contact. This would be similar to 1st Echelon tactics of large formations of spearmen or musketeers firing in volley form fixed formations that stand firm and do not give ground or break formations.
So a 'hard' stylist would operate individually similiary to the way a unit commander of Roman Spearmen/18th century army unit on a larger scale. Block hard, strike hard/in force, maintain a solid foundation/formation with a low mobility doctrine so that you can focus on pouring forceful attacks on the enemy.
"Soft" styles are more dynamic and rely on fluidity, speed and mobility in order to dictate the tempo of a fight and slip strikes into gaps in the opponent's defenses/attacks. This would be similar to guerilla warfare or high mobility/Combined Arms doctrine where small units infiltrate and attack supply lines, communications and do not focus on holding terrain as much as destroying the enemies ability to conduct war.
So a 'soft' stylist would operate individually similarly to the way a Mongul chieftain in charge of mounted bowmem/warriors/Company commander of light infantry woud on a larger scale. Strike fast/frequently from varying locations with a high tempo of mobility to make it difficult for the enemy to fix on you and deliver a solid blow. Constantly adjusting 'depth' and 'width' of your formation and contact distance to keep the enemy off balance - creating gaps that will expose weakness/soft spots in the enemies stance/formations.
In reality, these polarities do not exist, they are always 'yin/yanged' up so that there is an element of both extremes in a tactical application: The degree of emphasis will usually create the 'defined' doctrinal approach.
The other big difference between the two is that 'artists' will have a tendency to hold true to the 'art' over application almost like a faith where a 'tactician' will be willing to adapt/adopt practices that make him/herself more effective in the application phase. This goes back to the 'internal/external' contrast in focus between the two.
