Time base correction (TBC) for a VCR or used during VHS tape capture seems to relate mostly to correcting the Horizontal sync pulse and the length of the video line timing as it passes through a one or two line buffer.
A line buffer type of TBC was the most common until digital memory prices fell far enough to make field, or full frame "synchronizers" more practical.
What this means is a Level 1 - TBC (a small number of lines buffer tbc) would potentially "band" or stagger its fixes across the entire field and frame of the picture when it was output.. but usually it was unnoticeable unless scaled up, during which aliasing artifacts could appear. - This appears to be why it can be a good thing to disable an older "line-based" time base correcting circuit built-into a VCR when planning to capture and or scaling up a capture using an external device called a "scaler".
What this means is a Level 2 - TBC (only a field tbc) could potentially "jump" or de-sychronize between fields.. perceived more as a glitch, mostly depending on how bad the vertical sync retrace or VTI were between frames. Since "field based" tbcs were not on the market long before being replaced by the more expensive "full frame" capture time base correctors.. these problems are not as common as others. However they could produce a superior capture experince.. since they would not attempt to de-interlace the picture with an out dated poorer quality de-interlacing method.
What this means is a Level 3 - TBC (a full frame tbc) would normally be best.. with one exception, at some point the frame output (which may also perform a poor version of de-interlacing.. since that as a simpler output circuit than leaving it interlaced) may have to drop or repeat a frame in order to remain broadcast "locked" to a data frequency that matches broadcast standard.. while this could be minimized by using genlock.. it could also cause frame jumping vertically in a free running work flow with no genlock use. - While a free running full frame tbc would place that burden on the capture card.. since at some point it will have a a buffer over run or underrun.. and the capture card hardware or software will have to make a decision as to how to handle the situation.. its a choice.. of leaving the decision up to the TBC.. or leaving the choice up to the capture card.. as to how to handle the situation.
TBC - "time base correction" traditionally focused on "curing" problems with the Left "edge" or horizontal portion of the scan lines. While "genlock" or frame sychoonization focused on curing problems with the Top "edge" or the Top and Bottom edges of the field or frame as the field or frames were displayed and the next was setup by moving the focus of the scanning beam back to the top of the visual field.
So "tbc" is mostly about Left edge problems and "frame sync" is mostly about Top edge problems
When things go wrong,
A flag waving from the Upper Top Left edge is fixed using a TBC or a TBC that specifically "locks" its Left edge "frame clock" before additional lines are displayed.. a TBC that waits and samples more lines may "drift" back and forth releasing some of the Top Left lines before it settles down and locks. It "locks" fast.. as opposed to a broadcast TBC which is seeking to lock on an over the air transmission which may have additional problems related to signal ghosting and locks "slow". Some broadcast TBCs have a setting specifically to support use with a "VTR" in the studio environment.. that locks "fast".
A "vertically jumpy" or "rolling" problem is a frame sync problem and relates to stably outputting a field or frame at the right rate and time to match the expectations of the broadcast standard, or house timing genlock called a black burst.
Ideally and in practice.. a tbc does not do the job of a frame sync.. and a frame sync does not do the job of a tbc. They are two very different things. However some early devices for broadcast and for the consumer combined the two functions in a single box. Whether it actually did correct the Left "Edge" or not is often the question.
And they use digital computer memory to store different parts of the picture.
A tbc samples and stores and corrects and outputs line information.
A frame sync stores all of the "assumed" correct line information for a field or frame and outputs field or frame information.
Performing a tbc on the line information before its captured by the frame sync is important.. since it avoids over and under runs in the frame sync which can make problems with the vertical "jumps" and frame sync output "worse" if it is not performed.
TBC's for the most part are no longer made.. and if so its mostly for SDI.. or serial digital inteface output. All video signals are assumed to have already been converted to some digital format and are rendered analog only in exceptional circumstances and probably not likely to be broadcast in native form.
Frame synchronizers are still made and SD or HD versions are available, often with scalers. But these regularly go for many thousands of dollars used.
Video switchers and DVD recorders are looked upon as potential sources for TBC and Frame sync work.. as pass thru devices.. but for the most part are frame sync devices only. They "appear" to be time base correctors because they have to digitize the entire field.. but more often also de-interlace and output the complete frame.. the effect is the output can have many Left "edge" problems and problems with line length since those devices never attempted anything in the slightest to correct problems with line length. Worse.. the problems are "fixed" by simply "chopping off" badly timed lines and throwing the rest away.. baking in the problems.. from which there is no current way to recover missing information.
True "time base correctors" probably stopped being made about the year 2013 and the use in consumer projects and some commercial projects have probably accelerated the degradation of the supply in the used market.. making them all but unobtainable in good working condition. Some are servicing the short term electrolytic capacitors.. but these are rare and not often found.
FPGA efforts in the "line doubler world" or inexpensive "scaling" for the Gaming community for streaming is developing an ability to perform many of the functions of not only frame sync.. but also encroaching on the true - time base corrector realm as some older game consoles also had Left "edge" problems.