It's important to understand these concepts first:
Each position for the beam, table, and MLCs when the beam is on is called a "control point".
In forward planning, the dosimetrist sets up the beams at certain angles and preliminary blocks, simulates the dose delivered for those beams, and then adds and tweaks blocks to improve uniformity. This may be a single control point per beam, or multiple "field in field"/control points per beam (multiple sets of blocks). Traditionally the machine moves to its first control point, and delivers some number of monitor units (dose). Then it turns off and the collimator, MLCs, table, and/or gantry move (next control point or "field in field" if nothing but the collimators move). Then the machine turns back on again to deliver the next number of monitor units at the next control point. Conventionally, blocks were actual physical wedges or compensators (custom blocks), but modern linacs use the multi-leaf collimators (MLC) to make custom beam shapes. This is typically referred to as 3D-Conformal Radiation Therapy.
In inverse planning, the dosimetrist sets up a desired set of contraints (dose, dose uniformity, maximum dose, minimum dose, avoidance structures, etc), and the computer uses an optimization algorithm to set many control points (typically dozens) to make the dose plan fit the desired dose constraints. In static field IMRT using multiple "field in field", the dosimetrist sets a number of beam positions, and the software optimizes the MLC positions (multiple control points) for each beam position. This is typically referred to as Intensity Modulated Radiation Therapy (IMRT).
The more recent extension of IMRT is volumetric modulated arc therapy (VMAT). The gantry rotates through an arc or multiple arcs while the MLCs and dose rate change through a large number of control points, and the beam doesn't shut off during the arc. As you might imagine, these treatments are quite fast, as the machine doesn't have to start and stop with each control point.
A boost is specifically given to provide extra dose to a specific area, typically a region with a high risk of recurrence. Now that we do simultaneous integrated boosts, I can't give you a great definition that distinguishes a field-in-field from a boost. Maybe someone else can help?
A boost is a generic term referring to a higher dose given to some part of your initial field. Classically, this meant treating a large field (i.e. whole breast) to one dose (i.e. 50 Gy / 25 fractions) then sequentially, at the end of the all 25 fractions, treating a smaller field (i.e. tumor bed) to an additional dose (i.e. 10 Gy / 5 fractions). The total is 30 fractions.
This is often done as a "cone down", which is essentially using your initial beam/table positions, but with a smaller collimator size or custom MLCs that shrink down your field to some part of your initial field. Otherwise, your boost can be something entirely different. For example, if you're treating whole breast and boosting a superficial tumor bed, you can treat the whole breast with opposed matched tangents as normal, then switch to an en face electron field directed just at the tumor bed at the end for the boost.
Simultaneous integrated boost (SIB) is becoming popular in some other areas like head and neck. In head and neck, treatments are already performed with IMRT, and often are performed to 2-3 dose levels (i.e. 1-2 boosts). With SIB, the inverse planning of IMRT allows you enough freedom to be able to deliver different doses to different areas within your treatment field during *each treatment*. This is done again by the inverse planning algorithm optimizing many control points, which allow dose to be distributed differently throughout a structure as you specify.
So a typical SIB for head and neck might be something like that in RTOG 1016 (
http://www.rtog.org/ClinicalTrials/ProtocolTable/StudyDetails.aspx?study=1016).
70 Gy to gross disease in 2 Gy fractions (35 fractions)
56 Gy to high risk areas in 1.6 Gy fractions (35 fractions)
50 Gy to low risk areas in 1.43 Gy fractions (35 fractions)
The advantage of this is that the treatment is complete in 35 fractions, and that it only requires one plan. In a classic set of cone down boosts, you'd have to deliver 1.8 Gy x 25 fractions (45 Gy) to the whole area including low/high/gross, then cone down to 1.8 Gy x 4 more fractions (total of 52.2 Gy) to just the high/gross, then cone down again to another 1.8 Gy x 10 fractions to gross tumor (total of 70.2 Gy). This is complicated! With SIB, you don't need to boost two separate areas, which would require making two separate "boost plans".
The main disadvantage of the SIB is you end up with these funky dose fractionations. 1.43 Gy/fx is not a standard dose. So you do BED cals and convert your classic 1.8 Gy/fx doses into 1.43 Gy/fx doses. As above, notice I changed 1.8 Gy x 25 fractions = 45 Gy to low risk in conventional fractionation to the protocol's 1.43 Gy x 35 fx = 50 Gy. Based on the BEDs, these two schemes should be equivalent. But that is not a perfect science.