What does it mean for a bike to be inside-drifting versus outside-drifting?

Inside/Outside Drifting defined

These two terms refer specifically to how a vehicle will handle when you begin a drift; in particular, the direction it will shift.

• Inside drifting - the bike will shift (sharply) in the direction you are drifting. In some cases you will slide as far as 1/4* of width of the track.
• Outside drifting - the bike will turn in the direction you are drifting, but the center of gravity (like a real car) is near the rear, so the car will lurch "outward" in the opposite direction your are drifting. Generally outside drifting is more slippery than inside drifting, and a bike or kart may lurch as much as 1/2* of the width of the track.

^{* These numbers are an estimation, and should by no means be taken to be exact. It will also vary from one vehicle combination to another.}

Practical Differences

The main "practical" difference is how you need to approach turns, specifically long or sharp ones.

With inside drifting bikes you must always keep in mind how close you are to the edge of the track. It is best to approach a sharp bend from the outer-rim (or outer-middle) to avoid being shifted off the track.

On the other hand, with outside drifting, curves must be approached from the inner-rim or middle (at max), to avoid running off the track at the outer-rim.

Strategies

The drifting method you choose will be based upon the strategies you wish to employ or prioritize. Here are a few in brief.

• Collecting coins on bends - Use outside drifting. Inside drifting bikes will generally hug the inner-rim so tightly you'll glide by all of the coins, or at least most. It is possible to collect them efficiently with inside handling, but it requires careful planning ahead of time, and may in theory defeat the purpose of your sharp technique.

• Overtaking opponents and cutting sharp curves - Use inside drifting (obviously!) If your main concern is to have an aggressive lower-lane advantage then inside drifting is for you. The main advantage to lower lane is that the radius is smaller meaning a faster turn, and the ability to overcome opponents. If you use an outside drifting vehicle you need to be aware that you make easily loose a lead on a course with many bends.

• Taking long bends - Use outside drifting. Due to the sharpness of the angle that inside drifting bikes use, they have a tendency to drift in beyond there initial lurch. Therefore on long, especially gradual turns, if you hold it to long, you may drift off the inner-rim. Now, while outside drifting vehicles suffer this in an opposite manner, it is not as intense and much easier to control. As a final word, long bends are possible with an inside drifting vehicle, but are best broken into several smaller drifts, which may or may not harm performance depending on the situation.

• Building up mini-turbos - Use outside drifting. When a drift is held for a sufficient amount of time a mini-turbo will be granted. There are two levels: blue and a more powerful orange. The level gained is a successive process in time. Hold a drift, get a blue; hold it longer, get an orange. Inside drifting bikes will be at a disadvantage here, because due to the sharpness and speed they take turns, they won't have as much time to build up their mini turbos. An outside drifting vehicle will be more relaxed in this situation since it will by its very nature have a greater chance of drifting long enough to gain an orange boost. It should be noted that orange mini turbos are possible with inside drifting bikes; they just don't have the advantage outside drifting vehicles do.

Fire Hopping

There is one final point I'd like to discuss, and that is the concept of fire hopping. Essentially it is a technique used to make boosts (such as the ones from drifting mini-turbos) last longer. The technique requires a player to hop their vehicle by pressing ZR and is well documented in this answer.

This technique is only possible on outside drifting vehicles, and therefore if you choose to employ it (as many players already are) you will need to keep this in mind. On the other hand if you desire to build your strategy around an inside drifting style you will be at a potentially severe disadvantage. I will leave this up to you to evaluate yourself.

References

Most of the information from this post comes from actual player's opinions. I used these two threads from GameFAQs.com to serve as my basis, and I highly recommend you check them out. Anything else came from my own experience.

• I need advice for drifting. - GameFAQs
• What is a inward drift ? - GameFAQs