My first question to you is what type of shoes are you training in? Are they specific for the type of training that you do day in and day out? Think about it for a second. Now think about this, would you wear a basketball sneaker to run in? No probably not. If you are primarily training in a weight room then this may be some insight for you!
If you are primarily a weightlifter and are regularly performing any of the Olympic lifts (cleans, jerks, snatches) and are squatting then you might want to invest in a pair of weight lifting shoes. The average running shoe just doesn’t cut it, they are designed to absorb force and create a comfortable platform between your foot and the pavement.
Weight lifting shoes are designed to allow you to use all the force you can apply into the ground. The more force you can apply into the ground the more weight you can lift! The raised heel in weight lifting shoes gives you an advantage through increasing your ankle range of motion. The heel is designed to allow you to have a more upright torso while squatting which can then create a better activation of the correct musculature during the movement. They are also more stable than your average running shoe. This allows you to have a more consistent base to push or pull through during your lifts. Now there are many different brands of weightlifting shoes (I own a pair of inov8 fast lifts) so it would be personal preference based on your own foot and comfort for which one would be the best for you!
If your primary training consisted of some barbell movements, among many other movements, and does not consist of Olympic lifts then a cross trainer or "training sneaker" might be your best bet for a training shoe choice. A good cross trainer will have the qualities of a firm heel, good support (not too flimsy) and light weight. Again, these are more durable and stable than your average running shoe. Your training shoe should just be your training shoe.
The biggest difference that you will find with a training shoe is that it is designed with more lateral support and stability as well as more flexibility in the forefoot, as compared to a running shoe that is designed for primarily forward motion of heel to toe striking.
From my personal experience I will never train in a regular running shoe ever again after training and lifting in a cross trainer (I own a pair of Nike metcons). I feel more stable and honestly more comfortable during my workouts. This is not an advertisement to go but a pair of Nike metcons.
I do want you to think about what you do for your daily/weekly training and workouts. Do you have any ankle, knee and or hip pain? It might be time for a new pair of shoes that can help you bring your training to the next level! Also it's an excuse to buy a new pair of shoes. Who doesn’t like that! #Beaboutit