Yes, you can. There isn't any difference.

More important thing is the vigor of the rootstock. If possible, the vigor of both rootstock and scion should be similar, although you can successfully graft varieties of different vigor. I have done it without problems.

axier,
Hope you don't mind if I pick your brain a little more. If I am using a cutting to graft on to a 5 year old LSU Gold tree growing in a tub what grafting method would be best to use? Would grafting like I did apple and pear trees work?
Since the tree I am grafting to will have a thick limb and the scion will be much thinner would a cleft graft work?
Lou NE., PA

You have to stimulate the sprouting of new limbs and later to graft on it with the chip-budding method, in my opinion is the best method for figs. June is the best time although you can graft until August.

I have tried "T" budding and I don't advise it. Poor results and, if it takes, the development is much slower.

The figs are more difficult to graft than other fruit trees like apples and pears. Anyway, you can get an acceptable success rate with chip-budding.

You can see how to graft a fig in this link:

http://www.jardin-mundani.com/English/GRAFTS/Escutcheon-majorcan.htm

Here is a link that might be useful: Mundani's site

Lou, Figs are usually budded, but they can be grafted. I've never tried it, but there is a description of the process in Eisen's "The Fig" starting on page 143 of his book. He has pictures too.
http://books.google.com/books?id=IThJAAAAMAAJ&pg=PA279&lpg=PA279&dq=%22purple+smyrna%22&source=web&ots=UOuOeuefQ1&sig=XizVEixAWax8JK0w1ftedZYH6aQ
Wickson's "The California Fruits and How to Grow Them" also has a piece on grafting starting on page 327.

Here is a link that might be useful: Wickson's Grafting Instructions

Lou, I am an expert grafter at almost everything and I tried figs last spring for the first time using my usual tricks and got complete failure. So I concluded they need something special.

I am doing n-way figs this year not by grafting but by rooting 5 cuttings in one pot.

Scott

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Lou
I hope you get a lot of success in fig grafting. However, it will put a lot of onus on you to keep your grafted fig tree safe from unexpected low temperatures in your zone 5.

ottawan, From what is written, the fig has to be completely dormant for grafting to work. So being in zone 5 would actually be an advantage right now, LOL.

I am not a wizard nor an exceptional grafter, and I achieve very acceptable results with chip-budding in late spring to mid summer. Other methods than budding are unadvised by experts like Pierre Baud.

If you want to try other methods like grafting during dormant season or similar, it's up to you, but you probably will lose your time and you will give up. They fail a lot.

I know expert grafters who have tried the whip and crown grafting methods in figs, they are absolutely discouraging with very poor results. In the case of whip grafting 0% success.

You have mentioned apples and pears, they are in my opinion very easy to graft. You can achieve near 100% success with the most of grafting methods (crown grafting is my preferred in this case), but figs are other story.

If you follow, beside the usual advises for chip-budding, all of my advises in this post there is no reason to fail, surely you won't get a 100 % success but so a reasonable rate.

This one of my grafted adult figs, all the limbs from the 6 main branches are grafted. All except one (with "T" budding) have been grafted with chip-budding method:

Lou,
I have tried Axier method and the graft took. The problem was I didn't have support for the newly grafted branch that sprouted, and it broke off from the weight.
Remember don't graft it when dormant, the bark has to peel easily, and that only happens when the tree is actively growing.
Era condit mentioned in his book that grafting can be done by the cleft grafting method. but I haven't attempted that.

Bass

I have forgotten to say that there is another option. It is approach grafting:

It is a foolproof grafting method, but it is a little bit cumbersome. You need to have the scion like a rooted plant, and at least one of them, rootstock or scion, must be in a pot for approaching. You have to secure them firmly together for weeks.

The kind side of this method is that while the union in the graft is forming, the "scion" is nourished by own roots. So it is not a countdown, the graft can take all the time it needs to form the union.

I haven't tried it with figs, but it surely works.

Axier, I'm not advocating grafting over budding. Lou stated he was using a cutting and sometimes cuttings are thin, the buds involved very small, and not suitable for budding. I was just giving him information on the grafting process.
A version of the approach graft can be used if the scion is too thin for budding. It is called a "bottled" approach graft. A small bottle or large test tube is taped below the graft area and the scion put into water in the bottle. The process you posted above is then used. It's a good idea to put in some clean (very important) charcoal to keep the water fresh and check the water level daily. One advantage is it can be used after the plants have come out of dormancy. I've used this method successfully - but not with figs. So I can't comment on how likely it would succeed with figs.