If you simply walk into a gym and allow them to give you their sample programme, you'll most likely find yourself on a basic hypertrophy programme, one designed to build muscle (although, without the nutrition, recovery etc. it's unlikely to be effective).
In fact, although they overlap, there are different categories of resistance training you can work on. For this lesson, I've split this into 3 main categories, although you could argue for a different split, depending on your perspective.
Everything below is a very basic explanation. Athletes training specifically from strength sports use a number of advanced techniques that are not necessary for developing a healthy level of strength.
Maximum Strength
This is simply training the maximum amount of weight that you can lift for one repetition, although you would not do many sets in a year in which you get close to that maximum number.
The best example of a sport-specific context in which maximum strength is the key success factor is powerlifting
If you're lifting for maximum strength, you'd typically lift between one and three reps per set with rest periods of 5 minutes or more (fewer, heavier reps require longer rest periods). Between 3 & 5 sets is generally plenty of volume.
Two heavy sessions per week, done well, can be plenty for building and maintaining strength.
Although, most powerlifters are not small for their height, one benefit of training for maximum strength is that endurance athletes are not likely to gain huge amounts of bulky muscle.
Hypertrophy
Training for hypertrophy is training to build muscle mass. Sessions tend to be long and purposely exhausting. Along with optimising body composition, this is where bodybuilders excel.
Typical sets contain between eight and twelve reps and rest periods are fairly short. In the quest for exhaustion of muscles, sessions tend to have a focus on a small number of body parts and contain a fairly high number of sets. There are also a lot of advanced exercise techniques used to drive more muscle growth.
My bodybuilder buddies seem to be in the gym all the time.
Unless your sport requires lots of muscle mass, hypertrophy training probably isn't for you. In fact, unless it's your sport, the level of fatigue you'd have to deal with almost certainly makes hypertrophy training inappropriate for anyone who is not focused on building a physique, except perhaps for small strategic blocks here and there in the programme.
Strength Endurance
Endurance athletes are drawn to strength endurance because the focus on work capacity seems to match how endurance sports work. Enhancing strength endurance involves doing a lot of repetitions per set and minimising the rest periods.
Crossfit fits nicely into this mould. The top Crossfit guys have an awesome work capacity, but they seem to be in the gym an awful amount. Granted, Crossfit is their sport.
Again, this is a training area that is too specialist for an athlete's health-based training because it requires too much volume and the acceptance of a fairly high level of fatigue.
What Should You Choose?
Whilst there is significant crossover between all three categories - e.g. you will build muscle regardless of the approach - I'd recommend working primarily on maximum strength as your health-based resistance training.
Sessions can be shorter, fatigue & soreness is generally lower (although CNS fatigue can be high) and you can train far less frequently.